Quantitative distribution of parvalbumin, calretinin, and calbindin D-28k immunoreactive neurons in the visual cortex of normal and Alzheimer cases.

The distribution of parvalbumin (PV), calretinin (CR), and calbindin (CB) immunoreactive neurons was studied with the help of an image analysis system (Vidas/Zeiss) in the primary visual area 17 and associative area 18 (Brodmann) of Alzheimer and control brains. In neither of these areas was there a significant difference between Alzheimer and control groups in the mean number of PV, CR, or CB immunoreactive neuronal profiles, counted in a cortical column going from pia to white matter. Significant differences in the mean densities (numbers per square millimeter of cortex) of PV, CR, and CB immunoreactive neuronal profiles were not observed either between groups or areas, but only between superficial, middle, and deep layers within areas 17 and 18. The optical density of the immunoreactive neuropil was also similar in Alzheimer and controls, correlating with the numerical density of immunoreactive profiles in superficial, middle, and deep layers. The frequency distribution of neuronal areas indicated significant differences between PV, CR, and CB immunoreactive neuronal profiles in both areas 17 and 18, with more large PV than CR and CB positive profiles. There were also significantly more small and less large PV and CR immunoreactive neuronal profiles in Alzheimer than in controls. Our data show that, although the brain pathology is moderate to severe, there is no prominent decrease of PV, CR and CB positive neurons in the visual cortex of Alzheimer brains, but only selective changes in neuronal perikarya.

The algebraic equality of two asymptotic tests for the hypothesis that a normal distribution has a specified correlation matrix

It is proved the algebraic equality between Jennrich's (1970) asymptotic$X^2$ test for equality of correlation matrices, and a Wald test statisticderived from Neudecker and Wesselman's (1990) expression of theasymptoticvariance matrix of the sample correlation matrix.

The normal distribution in some constrained sample spaces

Phenomena with a constrained sample space appear frequently in practice. This is the case e.g. with strictly positive data, or with compositional data, like percentages or proportions. If the natural measure of difference is not the absolute one, simple algebraic properties show that it is more convenient to work with a geometry different from the usual Euclidean geometry in real space, and with a measure different from the usual Lebesgue measure, leading to alternative models which better fit the phenomenon under study. The general approach is presented and illustrated using the normal distribution, both on the positive real line and on the D-part simplex. The original ideas of McAlister in his introduction to the lognormal distribution in 1879, are recovered and updated

Alterations in neurofilament protein immunoreactivity in human hippocampal neurons related to normal aging and Alzheimer's disease.

The distribution of immunoreactivity for the neurofilament triplet class of intermediate filament proteins was examined in the hippocampus of young, adult and elderly control cases and compared to that of Alzheimer's disease cases. In a similar fashion to non-human mammalian species, pyramidal neurons in the CA1 region showed a very low degree of neurofilament triplet immunoreactivity in the three younger control cases examined. However, in the other control cases of 49 years of age and older, many CA1 pyramidal neurons showed elevated neurofilament immunoreactivity. In the Alzheimer's disease cases, most of the surviving CA1 neurons showed intense labeling for the neurofilament triplet proteins, with many of these neurons giving off abnormal "sprouting" processes. Double labeling demonstrated that many of these neurons contained tangle-like or granular material that was immunoreactive for abnormal forms of tau and stained with thioflavine S, indicating that these neurons are in a transitional degenerative stage. An antibody to phosphorylated neurofilament proteins labeled a subset of neurofibrillary tangles in the Alzheimer's disease cases. However, following formic acid pre-treatment, the number of neurofibrillary tangles showing phosphorylated neurofilament protein immunoreactivity increased, with double labeling confirming that all of the tau-immunoreactive neurofibrillary tangles were also immunoreactive for phosphorylated neurofilament proteins. Immunoblotting demonstrated that there was a proportionately greater amount of the neurofilament triplet subunit proteins in hippocampal tissue from Alzheimer's disease cases as compared to controls. These results indicate that there are changes in the cytoskeleton of CA1 neurons associated with age which are likely to involve an increase in the level of neurofilament proteins and may be a predisposing factor contributing towards their high degree of vulnerability in degenerative conditions such as Alzheimer's disease. The cellular factors affecting hippocampal neurons during aging may be potentiated in Alzheimer's disease to result in even higher levels of intracellular neurofilament proteins and the progressive alterations of neurofilaments and other cytoskeletal proteins that finally results in neurofibrillary tangle formation and cellular degeneration.

The normal distribution in some constrained sample spaces

Phenomena with a constrained sample space appear frequently in practice. This is the case e.g. with strictly positive data, or with compositional data, like percentages or proportions. If the natural measure of difference is not the absolute one, simple algebraic properties show that it is more convenient to work with a geometry different from the usual Euclidean geometry in real space, and with a measure different from the usual Lebesgue measure, leading to alternative models which better fit the phenomenon under study. The general approach is presented and illustrated using the normal distribution, both on the positive real line and on the D-part simplex. The original ideas of McAlister in his introduction to the lognormal distribution in 1879, are recovered and updated

Specific insulin and proinsulin in normal glucose tolerant first-degree relatives of NIDDM patients

In order to identify early abnormalities in non-insulin-dependent diabetes mellitus (NIDDM) we determined insulin (using an assay that does not cross-react with proinsulin) and proinsulin concentrations. The proinsulin/insulin ratio was used as an indicator of abnormal ß-cell function. The ratio of the first 30-min increase in insulin to glucose concentrations following the oral glucose tolerance test (OGTT; I30-0/G30-0) was taken as an indicator of insulin secretion. Insulin resistance (R) was evaluated by the homeostasis model assessment (HOMA) method. True insulin and proinsulin were measured during a 75-g OGTT in 35 individuals: 20 with normal glucose tolerance (NGT) and without diabetes among their first-degree relatives (FDR) served as controls, and 15 with NGT who were FDR of patients with NIDDM. The FDR group presented higher insulin (414 pmol/l vs 195 pmol/l; P = 0.04) and proinsulin levels (19.6 pmol/l vs 12.3 pmol/l; P = 0.03) post-glucose load than the control group. When these groups were stratified according to BMI, the obese FDR (N = 8) showed higher fasting and post-glucose insulin levels than the obese NGT (N = 9) (fasting: 64.8 pmol/l vs 7.8 pmol/l; P = 0.04, and 60 min post-glucose: 480.6 pmol/l vs 192 pmol/l; P = 0.01). Also, values for HOMA (R) were higher in the obese FDR compared to obese NGT (2.53 vs 0.30; P = 0.075). These results show that FDR of NIDDM patients have true hyperinsulinemia (which is not a consequence of cross-reactivity with proinsulin) and hyperproinsulinemia and no dysfunction of a qualitative nature in ß-cells.

Insulin secretion, insulin sensitivity, and hepatic insulin extraction in first-degree relatives of type 2 diabetic patients

To identify early metabolic abnormalities in type 2 diabetes mellitus, we measured insulin secretion, sensitivity to insulin, and hepatic insulin extraction in 48 healthy normal glucose-tolerant Brazilians, first-degree relatives of type 2 diabetic patients (FH+). Each individual was matched for sex, age, weight, and body fat distribution with a person without history of type 2 diabetes (FH-). Both groups were submitted to a hyperglycemic clamp procedure (180 mg/dl). Insulin release was evaluated in its two phases. The first was calculated as the sum of plasma insulin at 2.5, 5.0, 7.5, and 10.0 min after the beginning of glucose infusion, and the second as the mean plasma insulin level in the third hour of the clamp procedure. Insulin sensitivity index (ISI) was the mean glucose infusion rate in the third hour of the clamp experiment divided by the mean plasma insulin concentration during the same period of time. Hepatic insulin extraction was determined under fasting conditions and in the third hour of the clamp procedure as the ratio between C-peptide and plasma insulin levels. FH+ individuals did not differ from FH- individuals in terms of the following parameters [median (range)]: a) first-phase insulin secretion, 174 (116-221) vs 207 (108-277) µU/ml, b) second-phase insulin secretion, 64 (41-86) vs 53 (37-83) µU/ml, and c) ISI, 14.8 (9.0-20.8) vs 16.8 (9.0-27.0) mg kg-1 min-1/µU ml-1. Hepatic insulin extraction in FH+ subjects was similar to that of FH- ones at basal conditions (median, 0.27 vs 0.27 ng/µU) and during glucose infusion (0.15 vs 0.15 ng/µU). Normal glucose-tolerant Brazilian FH+ individuals well-matched with FH- ones did not show defects of insulin secretion, insulin sensitivity, or hepatic insulin extraction as tested by hyperglycemic clamp procedures.

Estimators and Tests based on Likelihood-Depth with Application to Weibull Distribution, Gaussian and Gumbel Copula

In dieser Arbeit werden mithilfe der Likelihood-Tiefen, eingeführt von Mizera und Müller (2004), (ausreißer-)robuste Schätzfunktionen und Tests für den unbekannten Parameter einer stetigen Dichtefunktion entwickelt. Die entwickelten Verfahren werden dann auf drei verschiedene Verteilungen angewandt. Für eindimensionale Parameter wird die Likelihood-Tiefe eines Parameters im Datensatz als das Minimum aus dem Anteil der Daten, für die die Ableitung der Loglikelihood-Funktion nach dem Parameter nicht negativ ist, und dem Anteil der Daten, für die diese Ableitung nicht positiv ist, berechnet. Damit hat der Parameter die größte Tiefe, für den beide Anzahlen gleich groß sind. Dieser wird zunächst als Schätzer gewählt, da die Likelihood-Tiefe ein Maß dafür sein soll, wie gut ein Parameter zum Datensatz passt. Asymptotisch hat der Parameter die größte Tiefe, für den die Wahrscheinlichkeit, dass für eine Beobachtung die Ableitung der Loglikelihood-Funktion nach dem Parameter nicht negativ ist, gleich einhalb ist. Wenn dies für den zu Grunde liegenden Parameter nicht der Fall ist, ist der Schätzer basierend auf der Likelihood-Tiefe verfälscht. In dieser Arbeit wird gezeigt, wie diese Verfälschung korrigiert werden kann sodass die korrigierten Schätzer konsistente Schätzungen bilden. Zur Entwicklung von Tests für den Parameter, wird die von Müller (2005) entwickelte Simplex Likelihood-Tiefe, die eine U-Statistik ist, benutzt. Es zeigt sich, dass für dieselben Verteilungen, für die die Likelihood-Tiefe verfälschte Schätzer liefert, die Simplex Likelihood-Tiefe eine unverfälschte U-Statistik ist. Damit ist insbesondere die asymptotische Verteilung bekannt und es lassen sich Tests für verschiedene Hypothesen formulieren. Die Verschiebung in der Tiefe führt aber für einige Hypothesen zu einer schlechten Güte des zugehörigen Tests. Es werden daher korrigierte Tests eingeführt und Voraussetzungen angegeben, unter denen diese dann konsistent sind. Die Arbeit besteht aus zwei Teilen. Im ersten Teil der Arbeit wird die allgemeine Theorie über die Schätzfunktionen und Tests dargestellt und zudem deren jeweiligen Konsistenz gezeigt. Im zweiten Teil wird die Theorie auf drei verschiedene Verteilungen angewandt: Die Weibull-Verteilung, die Gauß- und die Gumbel-Copula. Damit wird gezeigt, wie die Verfahren des ersten Teils genutzt werden können, um (robuste) konsistente Schätzfunktionen und Tests für den unbekannten Parameter der Verteilung herzuleiten. Insgesamt zeigt sich, dass für die drei Verteilungen mithilfe der Likelihood-Tiefen robuste Schätzfunktionen und Tests gefunden werden können. In unverfälschten Daten sind vorhandene Standardmethoden zum Teil überlegen, jedoch zeigt sich der Vorteil der neuen Methoden in kontaminierten Daten und Daten mit Ausreißern.

Normal distribution and confidence intervals

lecture for COMP6235

The effect of triacylglycerol fatty acid positional distribution on postprandial plasma metabolite and hormone responses in normal adult men

The present study has examined the possibility that the positional distribution of fatty acids on dietary triacyglycerol (TAG) influences the postprandial response to a liquid meal in adult subjects. Postprandial TAG, non-esterified fatty acids (NEFA), ketones, glucose, insulin and gastric inhibitory polypeptide (GIP) responses were monitored in sixteen normal adult male subjects over 6 h following consumption of test meals containing dietary TAG in which palmitic acid was predominantly on the sn-1 (Control) or sn-2 positions (Betapol). Plasma total TAG, chylomicron-rich TAG and chylomicron-poor TAG concentrations were identical in response to the two test meals. The peak increase (mean (SD)) in chylomicron TAG was 0.85 (0.46) mmol/l after the Control meal and 0.85 (0.42) mmol/l after the Betapol meal. Plasma glucose, insulin, GIP, NEFA and ketone concentrations were also very similar following the two meals. It is concluded that dietary TAG containing saturated fatty acids on the sn-2 position appear in plasma at a similar level and over a similar timescale to TAG in which saturated fatty acids are predominantly located on sn-1 or sn-3 positions. The results reported in the present study demonstrate that the positional distribution of fatty acids on dietary TAG is not an important determinant of postprandial lipaemia in adult male subjects, but do not exclude the possibility that different responses may occur when these dietary TAG are given long term.

Constructing the frequency and wave normal distribution of whistler-mode wave power

We introduce a new methodology that allows the construction of wave frequency distributions due to growing incoherent whistler-mode waves in the magnetosphere. The technique combines the equations of geometric optics (i.e. raytracing) with the equation of transfer of radiation in an anisotropic lossy medium to obtain spectral energy density as a function of frequency and wavenormal angle. We describe the method in detail, and then demonstrate how it could be used in an idealised magnetosphere during quiet geomagnetic conditions. For a specific set of plasma conditions, we predict that the wave power peaks off the equator at ~15 degrees magnetic latitude. The new calculations predict that wave power as a function of frequency can be adequately described using a Gaussian function, but as a function of wavenormal angle, it more closely resembles a skew normal distribution. The technique described in this paper is the first known estimate of the parallel and oblique incoherent wave spectrum as a result of growing whistler-mode waves, and provides a means to incorporate self-consistent wave-particle interactions in a kinetic model of the magnetosphere over a large volume.

A nonlinear regression model with skew-normal errors

In this paper we have discussed inference aspects of the skew-normal nonlinear regression models following both, a classical and Bayesian approach, extending the usual normal nonlinear regression models. The univariate skew-normal distribution that will be used in this work was introduced by Sahu et al. (Can J Stat 29:129-150, 2003), which is attractive because estimation of the skewness parameter does not present the same degree of difficulty as in the case with Azzalini (Scand J Stat 12:171-178, 1985) one and, moreover, it allows easy implementation of the EM-algorithm. As illustration of the proposed methodology, we consider a data set previously analyzed in the literature under normality.