Neville C. Weber

Common Slope Tests for Bivariate Errors‐in‐Variables Models

Summary Likelihood ratio tests are derived for bivariate normal structural relationships in the presence of group structure. These tests may also be applied to less restrictive models where only errors are assumed to be normally distributed. Tests for a common slope amongst those from several datasets are derived for three different cases – when the assumed ratio of error variances is the same across datasets and either known or unknown,and when the standardised major axis model is used. Estimation of the slope in the case where the ratio of error variances is unknown could be considered as a maximum likelihood grouping method. The derivations are accompanied by some small sample simulations,and the tests are applied to data arising from work on seed allometry.

Chronic cerebral hypoperfusion and impaired neuronal function in rats.

Background and Purpose Studies in acute cerebral ischemia have shown that reductions in cerebral blood flow of up to 50% do not lead to infarction or alterations in neuronal electric activity. Little is known about the effects of chronic reductions in cerebral blood flow. The purpose of this study was to evaluate neuronal electrophysiological function in brain that had been subjected to a chronic reduction of cerebral blood flow of less than 50%. Based on existing knowledge of thresholds of cerebral ischemia, neuronal electrophysiological function should be unaffected by hypoperfusion of this magnitude. Methods An arteriovenous fistula model in the rat was used to induce chronic cerebral hypoperfusion with reductions of cerebral blood flow of 25% to 50% as measured previously by 14C-labeled autoradiography. Using in vitro electrophysiological brain slice techniques, long-term potentiation in hippocampal CA1 neurons was examined extracellularly after 6 months of chronic noninfarctional cerebral hypoperfusion. Brains were also examined histologically at this time for evidence of cerebral infarction. Results There was no evidence of cerebral infarction. Longterm potentiation was produced in 9 of 12 control animals and only 2 of 8 hypoperfused animals. This difference was significant (P<.05) and demonstrated that long-term potentiation was impaired in animals with chronic hypoperfusion. Conclusions Noninfarctional reductions in cerebral blood flow of up to 50% do impair neuronal function in chronic cerebral ischemia, a result quite distinct from that seen in acute ischemia. The threshold for neuronal dysfunction in chronic cerebral hypoperfusion is lower than that found in acute cerebral ischemia, suggesting that duration as well as severity of ischemic insult determines cellular viability. Chronic hypoperfusion may lead to a noninfarctional state with impaired neuronal function, a category of chronic cerebral ischemia not previously identified.

Chronic cerebral hypoperfusion: pathological and behavioral consequences.

OBJECTIVE Although the effects of acute ischemic insults to the brain are well known, the effects related to chronic ischemia are poorly delineated. The pathological and behavioral changes induced by a chronic noninfarctional reduction in cerebral blood flow of 25 to 50% maintained for 6 months were assessed. METHODS In each of 18 male Sprague-Dawley rats, an arteriovenous fistula was created in the neck via an anastomosis between the right external jugular vein and the right common carotid artery to induce cerebral hypoperfusion. Nineteen age-matched animals comprised a control group. Six months after surgery, the animals were examined using light and electron microscopic techniques, as well as via a battery of behavioral tests (motor, open field, and T-maze). RESULTS Examination of the hippocampus by using light microscopy revealed disorganization of the CA1 sector with an increased number of astrocytes. Transmission electron microscopy of the CA1 region demonstrated neurons with increased lipofuscin pigment and central nucleoli and astrocytes with more numerous cytosolic mitochondria. Motor performance testing revealed no gross motor deficits, although open-field assessment demonstrated increased exploratory behavior in rats with fistulas. Finally, T-maze testing results suggested that errors in working memory were more common in rats undergoing chronic cerebral hypoperfusion (P < 0.05). CONCLUSIONS These findings suggest that chronic reductions in cerebral blood flow of a magnitude previously thought to be harmless to neurons (i.e., reduced by 25-50%) do alter neuronal structure and affect whole animal behavior. Such a scenario may be responsible for a symptomatology secondary to arteriovenous steal and severe carotid stenoses. The mechanisms are still unknown.

Estimation of the Covariance Matrix of the Least Squares regression Coefficients when the Disturbance Covariance Matrix is of Unknown Form

This paper deals with the problem of estimating the covariance matrix of the least-squares regression coefficients under heteroskedasticity and/or autocorrelation of unknown form. We consider an estimator proposed by White [17] and give a relatively simple proof of its consistency. Our proof is based on more easily verifiable conditions than those of White. An alternative estimator with improved small sample properties is also presented.

ON THE RATE OF CONVERGENCE IN THE STRONG LAW OF LARGE NUMBERS FOR ARRAYS

For sequences of independent and identically distributed random variables it is well known that the existence of the second moment implies the law of the iterated logarithm. We show that the of the iterated logarithm does not extend to arrays of independent and identically distributed random variables and we develop an analogous rate result for such arrays under finitefourth moments

On resampling techniques for regression models

Resampling techniques like the bootstrap are examined for functions of the parameters of a linear model. A weighted resampling method analogous to the weighted jackknife developed by Hinkley (1977) is proposed for regression models.

Chronic Cerebral Hypoperfusion Inhibits Calcium-Induced Long-term Potentiation in Rats

BACKGROUND AND PURPOSE Long-term potentiation (LTP) in the rat hippocampus induced by tetanic stimulation is impaired by chronic cerebral hypoperfusion. The effects of chronic cerebral hypoperfusion on other forms of LTP are unknown. Such data could help delineate the pathways of cellular alteration caused by chronic cerebral hypoperfusion. The in vitro phenomenon of calcium-induced LTP was thus examined in rat hippocampal CA1 cells that had undergone chronic hypoperfusion with a reduction in cerebral blood flow of between 25% and 50% maintained for 26 weeks. METHODS Ten Sprague-Dawley rats had a cervical arteriovenous fistula surgically constructed, and an additional 10 animals were used as age-matched controls. Hippocampal slices were prepared after 26 weeks of hypoperfusion, and in vitro extracellular field potential recordings were taken from the Schäffer collateral CA1 region. Properties of LTP induced through transient exposure to a hypercalcemic solution were analyzed. RESULTS LTP was impaired in animals with an arteriovenous fistula (P < .05). Control animals demonstrated potentiation lasting for the entire 2 hours of recording, whereas fistula animals showed only transient potentiation (< 60 minutes) before returning to baseline values. CONCLUSIONS Calcium-induced LTP is impaired by chronic cerebral hypoperfusion. This form of LTP is different from that induced by tetanic stimulation. It is the most sensitive test available for in vitro detection of the changes induced in neuronal function by chronic noninfarctional reductions in cerebral blood flow of 25% to 50% and may indicate that the most basic cellular parameters involving calcium homeostasis and metabolism are being altered. The precise mechanisms remain to be elucidated, and several postulates are discussed.

Robust estimation of precision matrices under cellwise contamination

There is a great need for robust techniques in data mining and machine learning contexts where many standard techniques such as principal component analysis and linear discriminant analysis are inherently susceptible to outliers. Furthermore, standard robust procedures assume that less than half the observation rows of a data matrix are contaminated, which may not be a realistic assumption when the number of observed features is large. The problem of estimating covariance and precision matrices under cellwise contamination is investigated. The use of a robust pairwise covariance matrix as an input to various regularisation routines, such as the graphical lasso, QUIC and CLIME is considered. A method that transforms a symmetric matrix of pairwise covariances to the nearest covariance matrix is used to ensure the input covariance matrix is positive semidefinite. The result is a potentially sparse precision matrix that is resilient to moderate levels of cellwise contamination. Since this procedure is not based on subsampling it scales well as the number of variables increases.

Long-term potentiation saturation in chronic cerebral hypoperfusion

Chronic reductions in cerebral blood flow (CBF) of between 25 and 50%, in the absence of cerebral infarction, lead to impairments in hippocampal in vitro long-term potentiation (LTP). This study set out to explore some of the properties of this impairment of LTP. LTP is an electrophysiological property known to occur in the hippocampus, a region known to be exquisitely sensitive to hypoxic or ischemic insults. Thus, assessing LTP is a novel way of assessing the effects of subtle ischemic insults. Five male Sprague-Dawley rats had arteriovenous fistulae created surgically in the neck to induce a state of chronic cerebral hypoperfusion (CCH) with the features described above. Five rats were used as age-matched controls. Twenty-six weeks after fistula formation, the animals were prepared for in vitro hippocampal recording in a submerged tissue bath. Extracellular field potentials were recorded at the Schaffer collateral-CA1 region, with a stimulus intensity that achieved a population spike amplitude of 1 mV. After tetanic stimulation, the frequency and magnitude of LTP was compared between control and fistula animals. All animals in both these groups demonstrated LTP in contradistinction to our previous work where LTP was impaired in fistula animals when a higher intensity of stimulation was used. This indicates that the structures that are associated with the initiation and maintenance of LTP (most probably the ischemia-sensitive CA1 pyramidal cells) are saturated as the stimulus intensity is increased. Thus, at this lower intensity of stimulation LTP is preserved in the fistula animals, but found to be impaired as the stimulus intensity is increased. Consequently, this study provides further information on this newly identified subtype of chronic cerebral ischemia which, in time, after further studies in humans, may help to redefine therapeutic indicators for the management of cerebral arteriovenous malformation and severe cerebrovascular disease.

The Wright-Fisher model with temporally varying selection and population size

The Wright-Fisher model is considered in the case where the population size is random and the magnitude of the selective advantage of one of the alleles varies with time. The central question addressed is the possibility of ultimate genetic polymorphism. Partial results are obtained in the general case and complete results in the case where the population size and selective advantage are not density dependent. Bounds on the fixation probability are obtained when the selective advantage is constant.