Kapteyn's theory of skew frequency, and orthogonal polynomials in one and two variables

Chapter 1. SKEW FREQUENCY • Chapter 2. PROPERTIES OF ORTHOGONAL POLYNOMIALS RELATED TO THEIR GENERATING FUNCTIONS • Chanter 3. ORTHOGONAL POLYNOMIALS IN TWO VARIABLE

Application of asymptotic expansions of maximum likelihood estimators errors to gravitational waves from binary mergers: the single interferometer case

In this paper we describe a new methodology to calculate analytically the error for a maximum likelihood estimate (MLE) for physical parameters from Gravitational wave signals. All the existing litterature focuses on the usage of the Cramer Rao Lower bounds (CRLB) as a mean to approximate the errors for large signal to noise ratios. We show here how the variance and the bias of a MLE estimate can be expressed instead in inverse powers of the signal to noise ratios where the first order in the variance expansion is the CRLB. As an application we compute the second order of the variance and bias for MLE of physical parameters from the inspiral phase of binary mergers and for noises of gravitational wave interferometers . We also compare the improved error estimate with existing numerical estimates. The value of the second order of the variance expansions allows to get error predictions closer to what is observed in numerical simulations. It also predicts correctly the necessary SNR to approximate the error with the CRLB and provides new insight on the relationship between waveform properties SNR and estimation errors. For example the timing match filtering becomes optimal only if the SNR is larger than the kurtosis of the gravitational wave spectrum

‘But I’ve been teaching for 20 years…’: encouraging teaching accreditation for experienced staff working in higher education

The status of teaching and learning is an issue those providing and supporting higher education grapple with. The UK Higher Education Academy offers accreditation aligned to the professional standards framework (PSF). The PSF contextualises the role of teaching and supporting learning, and offers a mechanism for individuals’ commitment to be recognised. Here, we present a case-study of 19 established academics who reflected on their experiences of gaining recognition through their university’s accreditation scheme. Respondents prioritised institutional structures and outcomes such as student recruitment, job security, and status as drivers for engagement. Institutional leadership was significant in driving the accreditation agenda

Stochastic models in population biology and their deterministic analogs

In this paper we introduce a class of stochastic population models based on "patch dynamics". The size of the patch may be varied, and this allows one to quantify the departures of these stochastic models from various mean field theories, which are generally valid as the patch size becomes very large. These models may be used to formulate a broad range of biological processes in both spatial and non-spatial contexts. Here, we concentrate on two-species competition. We present both a mathematical analysis of the patch model, in which we derive the precise form of the competition mean field equations (and their first order corrections in the non-spatial case), and simulation results. These mean field equations differ, in some important ways, from those which are normally written down on phenomenological grounds. Our general conclusion is that mean field theory is more robust for spatial models than for a single isolated patch. This is due to the dilution of stochastic effects in a spatial setting resulting from repeated rescue events mediated by inter-patch diffusion. However, discrete effects due to modest patch sizes lead to striking deviations from mean field theory even in a spatial setting.Comment: 47 pages, 9 figure

Incidence, time course and predictors of impairments relating to caring for the profoundly affected arm after stroke: A systematic review

Background and purpose - A significant number of stroke survivors will not recover the use of their affected arm. A proportion will experience pain, stiffness and difficulty with basic care activities. The purpose of the review was to identify predictors of difficulty caring for the profoundly affected arm and establish the incidence and time-course of the related impairments of pain, spasticity and contracture. Method - Data sources: Databases (PubMED, MEDLINE, AMED, EMBASE, CINAHL and the Cochrane Controlled Trials Register) were searched from inception to December 2013. Additional studies were identified from citation tracking. Review methods: Independent reviewers used pre-defined criteria to identify eligible studies. Quality assessment and risk of bias were assessed using the McMasters Assessment Tool. A narrative evidence synthesis was performed. Results - Thirty-nine articles reporting 34 studies were included. No studies formally measured difficulty caring for the arm, but related impairments were common. Incidence of spasticity in those with weakness ranged from 33% to 78%, shoulder pain affected 22% to 90% and contracture was present in at least 50%. Spasticity and pain appear within 1 week of stroke, and contracture within two weeks. Impairments continued to develop over at least 3–6 months. The most frequent predictors of spasticity and contracture were weakness and reduced motor control, and the risk of pain is most commonly predicted by reduced sensation, shoulder subluxation, weakness and stroke severity. Discussion - There is no published evidence on predicting the likelihood of difficulty caring for the arm following stroke. However, the related impairments of spasticity, pain and contracture are common. Given the time-course of development, clinicians may need not only to intervene early but also be prepared to act over a longer time period. Further research is needed to examine difficulty caring for the arm and the relationship with associated impairments to enable researchers and clinicians to develop targeted interventions

Discrete Pearson distributions

These distributions are generated by a first order recursive scheme which equates the ratio of successive probabilities to the ratio of two corresponding quadratics. The use of a linearized form of this model will produce equations in the unknowns matched by an appropriate set of moments (assumed to exist). Given the moments we may find valid solutions. These are two cases; (1) distributions defined on the non-negative integers (finite or infinite) and (2) distributions defined on negative integers as well. For (1), given the first four moments, it is possible to set this up as equations of finite or infinite degree in the probability of a zero occurrence, the sth component being a product of s ratios of linear forms in this probability in general. For (2) the equation for the zero probability is purely linear but may involve slowly converging series; here a particular case is the discrete normal. Regions of validity are being studied. 11 refs

Resting-State Brain Functional Connectivity Is Altered in Type 2 Diabetes

Type 2 diabetes mellitus (T2DM) is a risk factor for Alzheimer disease (AD). Populations at risk for AD show altered brain activity in the default mode network (DMN) before cognitive dysfunction. We evaluated this brain pattern in T2DM patients. We compared T2DM patients (n = 10, age = 56 ± 2.2 years, fasting plasma glucose [FPG] = 8.4 ± 1.3 mmol/L, HbA1c = 7.5 ± 0.54%) with nondiabetic age-matched control subjects (n = 11, age = 54 ± 1.8 years, FPG = 4.8 ± 0.2 mmol/L) using resting-state functional magnetic resonance imaging to evaluate functional connectivity strength among DMN regions. We also evaluated hippocampal volume, cognition, and insulin sensitivity by homeostasis model assessment of insulin resistance (HOMA-IR). Control subjects showed stronger correlations versus T2DM patients in the DMN between the seed (posterior cingulate) and bilateral middle temporal gyrus (β = 0.67 vs. 0.43), the right inferior and left medial frontal gyri (β = 0.75 vs. 0.54), and the left thalamus (β = 0.59 vs. 0.37), respectively, with no group differences in cognition or hippocampal size. In T2DM patients, HOMA-IR was inversely correlated with functional connectivity in the right inferior frontal gyrus and precuneus. T2DM patients showed reduced functional connectivity in the DMN compared with control subjects, which was associated with insulin resistance in selected brain regions, but there were no group effects of brain structure or cognition

Analysis of schizophrenia-related genes and electrophysiological measures reveals ZNF804A association with amplitude of P300b elicited by novel sounds

Several genes have recently been identified as risk factors for schizophrenia (SZ) by genome-wide association studies (GWAS), including ZNF804A which is thought to function in transcriptional regulation. However, the downstream pathophysiological changes that these genes confer remain to be elucidated. In 143 subjects (68 clinical high risk, first episode or chronic cases; 75 controls), we examined the association between 21 genetic markers previously identified by SZ GWAS or associated with putative intermediate phenotypes of SZ against three event-related potential (ERP) measures: mismatch negativity (MMN), amplitude of P300 during an auditory oddball task, and P300 amplitude during an auditory novelty oddball task. Controlling for age and sex, significant genetic association surpassing Bonferroni correction was detected between ZNF804A marker rs1344706 and P300 amplitude elicited by novel sounds (beta=4.38, P=1.03 × 10−4), which is thought to index orienting of attention to unexpected, salient stimuli. Subsequent analyses revealed that the association was driven by the control subjects (beta=6.35, P=9.08 × 10−5), and that the risk allele was correlated with higher novel P300b amplitude, in contrast to the significantly lower amplitude observed in cases compared to controls. Novel P300b amplitude was significantly correlated with a neurocognitive measure of auditory attention under interference conditions, suggesting a relationship between novel P300b amplitude and higher-order attentional processes. Our results suggest pleiotropic effects of ZNF804A on risk for SZ and neural mechanisms that are indexed by the novel P300b ERP component