Do β-amyloid (Aβ) deposits in patients with Alzheimer's disease and Down's syndrome grow according to the log-normal model?

The size frequency distributions of diffuse, primitive and classic β- amyloid (Aβ) deposits were studied in single sections of cortical tissue from patients with Alzheimer's disease (AD) and Down's syndrome (DS) and compared with those predicted by the log-normal model. In a sample of brain regions, these size distributions were compared with those obtained by serial reconstruction through the tissue and the data used to adjust the size distributions obtained in single sections. The adjusted size distributions of the diffuse, primitive and classic deposits deviated significantly from a log-normal model in AD and DS, the greatest deviations from the model being observed in AD. More Aβ deposits were observed close to the mean and fewer in the larger size classes than predicted by the model. Hence, the growth of Aβ deposits in AD and DS does not strictly follow the log-normal model, deposits growing to within a more restricted size range than predicted. However, Aβ deposits grow to a larger size in DS compared with AD which may reflect differences in the mechanism of Aβ formation.

Size distribution curves of senile plaques in patients with Alzheimer’s disease: do plaques grow according to the log-normal model?

The size frequency distributions of diffuse, primitive and cored senile plaques (SP) were studied in single sections of the temporal lobe from 10 patients with Alzheimer’s disease (AD). The size distribution curves were unimodal and positively skewed. The size distribution curve of the diffuse plaques was shifted towards larger plaques while those of the neuritic and cored plaques were shifted towards smaller plaques. The neuritic/diffuse plaque ratio was maximal in the 11 – 30 micron size class and the cored/ diffuse plaque ratio in the 21 – 30 micron size class. The size distribution curves of the three types of plaque deviated significantly from a log-normal distribution. Distributions expressed on a logarithmic scale were ‘leptokurtic’, i.e. with excess of observations near the mean. These results suggest that SP in AD grow to within a more restricted size range than predicted from a log-normal model. In addition, there appear to be differences in the patterns of growth of diffuse, primitive and cored plaques. If neuritic and cored plaques develop from earlier diffuse plaques, then smaller diffuse plaques are more likely to be converted to mature plaques.

Pattern visual evoked potentials in man and tetrahydrobiopterin metabolism

The P2 visual evoked response in man has a cholinergic component while the P100 response has not. The P100 latency is significantly decreased after an oral dose of phenylalanine in man while the P2 signal is unaffected. Analyses of the P100 decrease shows no correlation with tyrosine levels but a significant positive correlation with plasma ane urine levels. A small group shows a P100 delay which correlated with increased neopterin levels only. Increased plasma total biopterins in man following a phenylalanine dose are due to rapidly increased tetrahydrobiopterin synthesis in the liver.

Appearance of bound states in random potentials with applications to soliton theory

We analyze the stochastic creation of a single bound state (BS) in a random potential with a compact support. We study both the Hermitian Schrödinger equation and non-Hermitian Zakharov-Shabat systems. These problems are of special interest in the inverse scattering method for Korteveg–de-Vries and the nonlinear Schrödinger equations since soliton solutions of these two equations correspond to the BSs of the two aforementioned linear eigenvalue problems. Analytical expressions for the average width of the potential required for the creation of the first BS are given in the approximation of delta-correlated Gaussian potential and additionally different scenarios of eigenvalue creation are discussed for the non-Hermitian case.

Automated assessment of visual fields and their inter-relation to evoked potentials in visual disorders

The Octopus Automated Perimeter was validated in a comparative study and found to offer many advantages in the assessment of the visual field. The visual evoked potential was investigated in an extensive study using a variety of stimulus parameters to simulate hemianopia and central visual field defects. The scalp topography was recorded topographically and a technique to compute the source derivation of the scalp potential was developed. This enabled clarification of the expected scalp distribution to half field stimulation using different electrode montages. The visual evoked potential following full field stimulation was found to be asymmetrical around the midline with a bias over the left occiput particularly when the foveal polar projections of the occipital cortex were preferentially stimulated. The half field response reflected the distribution asymmetry. Masking of the central 3° resulted in a response which was approximately symmetrical around the midline but there was no evidence of the PNP-complex. A method for visual field quantification was developed based on the neural representation of visual space (Drasdo and Peaston 1982) in an attempt to relate visual field depravation with the resultant visual evoked potentials. There was no form of simple, diffuse summation between the scalp potential and the cortical generators. It was, however, possible to quantify the degree of scalp potential attenuation for M-scaled full field stimuli. The results obtained from patients exhibiting pre-chiasmal lesions suggested that the PNP-complex is not scotomatous in nature but confirmed that it is most likely to be related to specific diseases (Harding and Crews 1982). There was a strong correlation between the percentage information loss of the visual field and the diagnostic value of the visual evoked potential in patients exhibiting chiasmal lesions.

Study of the cholinergic factors affecting the flash and pattern reversal visual evoked potentials

The effects of cholinergic agents undergoing clinical trials for the treatment of Alzheimer's disease and the anticholinergic agent scopolamine, were investigated on the components of the flash and pattern reversal visual evoked potentials (VEPs) in young healthy volunteers. The effect of recording the flash and pattern reversal VEPs for 13 hours in 5 healthy male volunteers, revealed no statistically significant change in the latency or amplitude measures. Administration of the muscarinic agonist SDZ 210-086 to 16 healthy male volunteers resulted in the reduction of the flash N2-P2 and pattern reversal N75-P100 peak-to-peak amplitudes. These effects on the flash VEP occurred at both doses (0.5 and 1.0 mg/day), but only at the higher dose on the pattern reversal VEP. Administration of the antimuscarinic agent scopolamine to 11 healthy young male volunteers, resulted in a delay of the flash P2 latency but no effect on the pattern reversal P100 latency. The pattern reversal N75-P100 peak-to-peak amplitude was also increased post dosing. The combination of scopolamine with the acetylcholinesterase inhibitor SDZ ENA 713 resulted in no significant effect on the flash and pattern reversal VEPs, suggesting that the effects of scopolamine may have been partially reversed. Topical application of scopolamine in 6 young healthy volunteers also resulted in no statistically significant effects on the flash and pattern reversal VEPs. The selective effect of scopolamine on the flash P2 latency but not on the pattern reversal P100 latency, provided a model whereby new cholinergic agents developed for the treatment of Alzheimer's disease can be investigated on a physiological basis. In addition, the results of this study led to the hypothesis that the selective flash P2 delay in Alzheimer's disease was probably due to a cholinergic deficit in both the tectal pathway from the retina to the visual cortex and the magnocellular path of the geniculostriate pathway, whereas the lack of an effect on the pattern reversal P100 component was probably due to a sparing of the parvocellular geniculostriate pathway.

Topographic studies of scalp potentials evoked by pattern presentation

The waveform and scalp distribution of the visual evoked potentials elicited by stimuli in the foveal and parafoveal regions have been investigated in a group of normal humans using a 16-channel `brain mapping' system. The waveform and topography of the responses to pattern onset and pattern reversal stimulation were investigated, using 4 x 4o full field and 4 x 2o lateral and altitudinal half-field stimuli. The responses were composed of several successive peaks which are in some respects consistent with those demonstrated by other workers using larger field sizes. The differences in the behaviour of these components with respect to the position of the stimulus in the visual field were suggestive of origins in different areas of the visual cortex and/or different visual mechanism. Of particular interest were the major early positive components `P90' and `P95' of the responses to pattern onset and pattern reversal stimulation respectively. More detailed exploration of the behaviour of these major early positive components was carried out using `M-scaled' stimuli selected to activate one square centimetre patches of striate cortex and associated extrastriate re-projections, positioned at different points in the foveal and parafoveal area of the visual field. The inter- and intra-subject variability in amplitude and localisation of the signals elicited by these targets was considered to be a reflection of the individual variations in relationship of visual field projections with the pattern of gyri and fissures on the proximal surface of the occipital lobe. The behaviour of component P90 of the onset response is consistent with a lateral origin in extrastriate visual cortex; that of P95 of the pattern reversal response is consistent in some respects with a striate cortical origin, but in others with a partial origin in extrastriate cortex.

The clinical utility of the middle latency and 40Hz auditory evoked potentials in audiological electrodiagnosis

The two elcctrophysiological tests currently favoured in the clinical measurement of hearing threshold arc the brainstorm evoked potential (BAEP) and the slow vertex response (SVR). However, both tests possess disadvantages. The BAEP is the test of choice in younger patients as it is stable at all levels of arousal, but little information has been obtained to date at a range of frequencies. The SVR is frequency specific but is unreliable in certain adult subjects and is unstable during sleep or in young children. These deficiencies have prompted research into a third group of potentials, the middle latency response (MLR) and the 40HZ responses. This research has compared the SVR and 40HZ response in waking adults and reports that the 40HZ test can provide a viable alternative to the SVR provided that a high degree of subject relaxation is ensured. A second study examined the morphology of the MLR and 40HZ during sleep. This work suggested that these potentials arc markedly different during sleep and that methodological factors have been responsible for masking these changes in previous studies. The clinical possibilities of tone pip BAEPs were then examined as these components were proved to be the only stable responses present in sleep. It was found that threshold estimates to 5OOHz, lOOOHz and 4000Hz stimuli could be made to within 15dBSL in most cases. A final study looked more closely at methods of obtaining frequency specific information in sleeping subjects. Threshold estimates were made using established BAEP parameters and this was compared to a 40HZ procedure which recorded a series of BAEPs over a 100msec. time sweep. Results indicated that the 40mHz procedure was superior to existing techniques in estimating threshold to low frequency stimuli. This research has confirmed a role for the MLR and 40Hz response as alternative measures of hearing capability in waking subjects and proposes that the 40Hz technique is useful in measuring frequency specific thresholds although the responses recorded derive primarily from the brainstem.

Biases in approximating log production

Most empirical work in economic growth assumes either a Cobb–Douglas production function expressed in logs or a log-approximated constant elasticity of substitution specification. Estimates from each are likely biased due to logging the model and the latter can also suffer from approximation bias. We illustrate this with a successful replication of Masanjala and Papagerogiou (The Solow model with CES technology: nonlinearities and parameter heterogeneity, Journal of Applied Econometrics 2004; 19: 171–201) and then estimate both models in levels to avoid these biases. Our estimation in levels gives results in line with conventional wisdom.

Testing for financial crashes using the Log Periodic Power Law model

Many papers claim that a Log Periodic Power Law (LPPL) model fitted to financial market bubbles that precede large market falls or 'crashes', contains parameters that are confined within certain ranges. Further, it is claimed that the underlying model is based on influence percolation and a martingale condition. This paper examines these claims and their validity for capturing large price falls in the Hang Seng stock market index over the period 1970 to 2008. The fitted LPPLs have parameter values within the ranges specified post hoc by Johansen and Sornette (2001) for only seven of these 11 crashes. Interestingly, the LPPL fit could have predicted the substantial fall in the Hang Seng index during the recent global downturn. Overall, the mechanism posited as underlying the LPPL model does not do so, and the data used to support the fit of the LPPL model to bubbles does so only partially. © 2013.

Statnote 35: are the data log-normal?

In many of the Statnotes described in this series, the statistical tests assume the data are a random sample from a normal distribution These Statnotes include most of the familiar statistical tests such as the ‘t’ test, analysis of variance (ANOVA), and Pearson’s correlation coefficient (‘r’). Nevertheless, many variables exhibit a more or less ‘skewed’ distribution. A skewed distribution is asymmetrical and the mean is displaced either to the left (positive skew) or to the right (negative skew). If the mean of the distribution is low, the degree of variation large, and when values can only be positive, a positively skewed distribution is usually the result. Many distributions have potentially a low mean and high variance including that of the abundance of bacterial species on plants, the latent period of an infectious disease, and the sensitivity of certain fungi to fungicides. These positively skewed distributions are often fitted successfully by a variant of the normal distribution called the log-normal distribution. This statnote describes fitting the log-normal distribution with reference to two scenarios: (1) the frequency distribution of bacterial numbers isolated from cloths in a domestic environment and (2), the sizes of lichenised ‘areolae’ growing on the hypothalus of Rhizocarpon geographicum (L.) DC.

Multi-level visualisation using Gaussian process latent variable models

Projection of a high-dimensional dataset onto a two-dimensional space is a useful tool to visualise structures and relationships in the dataset. However, a single two-dimensional visualisation may not display all the intrinsic structure. Therefore, hierarchical/multi-level visualisation methods have been used to extract more detailed understanding of the data. Here we propose a multi-level Gaussian process latent variable model (MLGPLVM). MLGPLVM works by segmenting data (with e.g. K-means, Gaussian mixture model or interactive clustering) in the visualisation space and then fitting a visualisation model to each subset. To measure the quality of multi-level visualisation (with respect to parent and child models), metrics such as trustworthiness, continuity, mean relative rank errors, visualisation distance distortion and the negative log-likelihood per point are used. We evaluate the MLGPLVM approach on the ‘Oil Flow’ dataset and a dataset of protein electrostatic potentials for the ‘Major Histocompatibility Complex (MHC) class I’ of humans. In both cases, visual observation and the quantitative quality measures have shown better visualisation at lower levels.

On the hydrophobicity of peptides:comparing empirical predictions of peptide log P values

Peptides are of great therapeutic potential as vaccines and drugs. Knowledge of physicochemical descriptors, including the partition coefficient logP, is useful for the development of predictive Quantitative Structure-Activity Relationships (QSARs). We have investigated the accuracy of available programs for the prediction of logP values for peptides with known experimental values obtained from the literature. Eight prediction programs were tested, of which seven programs were fragment-based methods: XLogP, LogKow, PLogP, ACDLogP, AlogP, Interactive Analysis's LogP and MlogP; and one program used a whole molecule approach: QikProp. The predictive accuracy of the programs was assessed using r(2) values, with ALogP being the most effective (r( 2) = 0.822) and MLogP the least (r(2) = 0.090). We also examined three distinct types of peptide structure: blocked, unblocked, and cyclic. For each study (all peptides, blocked, unblocked and cyclic peptides) the performance of programs rated from best to worse is as follows: all peptides - ALogP, QikProp, PLogP, XLogP, IALogP, LogKow, ACDLogP, and MlogP; blocked peptides - PLogP, XLogP, ACDLogP, IALogP, LogKow, QikProp, ALogP, and MLogP; unblocked peptides - QikProp, IALogP, ALogP, ACDLogP, MLogP, XLogP, LogKow and PLogP; cyclic peptides - LogKow, ALogP, XLogP, MLogP, QikProp, ACDLogP, IALogP. In summary, all programs gave better predictions for blocked peptides, while, in general, logP values for cyclic peptides were under-predicted and those of unblocked peptides were over-predicted.

Long memory in log-range series:do structural breaks matter?

This paper examines whether the observed long memory behavior of log-range series is to some extent spurious and whether it can be explained by the presence of structural breaks. Utilizing stock market data we show that the characterization of log-range series as long memory processes can be a strong assumption. Moreover, we find that all examined series experience a large number of significant breaks. Once the breaks are accounted for, the volatility persistence is eliminated. Overall, the findings suggest that volatility can be adequately represented, at least in-sample, through a multiple breaks process and a short run component.