Cerebellar mechanisms for motor learning: Testing predictions from a large-scale computer simulation

The cerebellum is the major brain structure that contributes to our ability to improve movements through learning and experience. We have combined computer simulations with behavioral and lesion studies to investigate how modification of synaptic strength at two different sites within the cerebellum contributes to a simple form of motor learning—Pavlovian conditioning of the eyelid response. These studies are based on the wealth of knowledge about the intrinsic circuitry and physiology of the cerebellum and the straightforward manner in which this circuitry is engaged during eyelid conditioning. Thus, our simulations are constrained by the well-characterized synaptic organization of the cerebellum and further, the activity of cerebellar inputs during simulated eyelid conditioning is based on existing recording data. These simulations have allowed us to make two important predictions regarding the mechanisms underlying cerebellar function, which we have tested and confirmed with behavioral studies. The first prediction describes the mechanisms by which one of the sites of synaptic modification, the granule to Purkinje cell synapses (gr → Pkj) of the cerebellar cortex, could generate two time-dependent properties of eyelid conditioning—response timing and the ISI function. An empirical test of this prediction using small, electrolytic lesions of the cerebellar cortex revealed the pattern of results predicted by the simulations. The second prediction made by the simulations is that modification of synaptic strength at the other site of plasticity, the mossy fiber to deep nuclei synapses (mf → nuc), is under the control of Purkinje cell activity. The analysis predicts that this property should confer mf → nuc synapses with resistance to extinction. Thus, while extinction processes erase plasticity at the first site, residual plasticity at mf → nuc synapses remains. The residual plasticity at the mf → nuc site confers the cerebellum with the capability for rapid relearning long after the learned behavior has been extinguished. We confirmed this prediction using a lesion technique that reversibly disconnected the cerebellar cortex at various stages during extinction and reacquisition of eyelid responses. The results of these studies represent significant progress toward a complete understanding of how the cerebellum contributes to motor learning. ^

Assessment of the effect on statistical power of regression model misspecification by using techniques of mathematical statistics and simulation study

Objectives. This paper seeks to assess the effect on statistical power of regression model misspecification in a variety of situations. ^ Methods and results. The effect of misspecification in regression can be approximated by evaluating the correlation between the correct specification and the misspecification of the outcome variable (Harris 2010).In this paper, three misspecified models (linear, categorical and fractional polynomial) were considered. In the first section, the mathematical method of calculating the correlation between correct and misspecified models with simple mathematical forms was derived and demonstrated. In the second section, data from the National Health and Nutrition Examination Survey (NHANES 2007-2008) were used to examine such correlations. Our study shows that comparing to linear or categorical models, the fractional polynomial models, with the higher correlations, provided a better approximation of the true relationship, which was illustrated by LOESS regression. In the third section, we present the results of simulation studies that demonstrate overall misspecification in regression can produce marked decreases in power with small sample sizes. However, the categorical model had greatest power, ranging from 0.877 to 0.936 depending on sample size and outcome variable used. The power of fractional polynomial model was close to that of linear model, which ranged from 0.69 to 0.83, and appeared to be affected by the increased degrees of freedom of this model.^ Conclusion. Correlations between alternative model specifications can be used to provide a good approximation of the effect on statistical power of misspecification when the sample size is large. When model specifications have known simple mathematical forms, such correlations can be calculated mathematically. Actual public health data from NHANES 2007-2008 were used as examples to demonstrate the situations with unknown or complex correct model specification. Simulation of power for misspecified models confirmed the results based on correlation methods but also illustrated the effect of model degrees of freedom on power.^

Performance enhancement of large industrial wastewater stabilization ponds

A 6-month-long, bench-scale simulation of an industrial wastewater stabilization pond (WSP) system was conducted to evaluate responses to several potential performance-enhancing treatments. The industrial WSP system consists of an anaerobic primary (1ry) WSP treating high-strength wastewater, followed by facultative secondary (2ry) and aerobic tertiary (3ry) WSPs in series treating lower-strength wastewater. The 1ry WSP was simulated with four glass aquaria which were fed with wastewater from the actual WSP system. The treatments examined were phosphorus supplementation (PHOS), phosphorus supplementation with pH control (PHOS+ALK), and phosphorus supplementation with pH control and effluent recycle (PHOS+ALK+RCY). The supplementary phosphorus treatment alone did not yield any significant change versus the CONTROL 1ry model pond. The average carbon to phosphorus ratio of the feed wastewater received from the WSP system was already 100:0.019 (i.e., 2,100 mg/l: 0.4 mg/l). The pH-control treatments (PHOS+ALK and PHOS+ALK+RCY) produced significant results, with 9 to 12 percent more total organic carbon (TOC) removal, 43 percent more volatile organic acid (VOA) generation, 78 percent more 2-ethoxyethanol and 14 percent more bis(2-chloroethyl)ether removal, and from 100- to 10,000-fold increases in bacterial enzyme activity and heterotrophic bacterial numbers. Recycling a 10-percent portion of the effluent yielded less variability for certain physicochemical parameters in the PHOS+ALK+RCY 1ry model pond, but overall there was no statistically-detectable improvement in performance versus no recycle. The 2ry and 3ry WSPs were also simulated in the laboratory to monitor the effect and fate of increased phosphorus loadings, as might occur if supplemental phosphorus were added to the 1ry WSP. Noticeable increases in algal growth were observed at feed phosphorus concentrations of 0.5 mg/l; however, there were no significant changes in the monitored physicochemical parameters. The effluent phosphorus concentrations from both the 2ry and 3ry model ponds did increase notably when feed phosphorus concentrations were increased from 0.5 to 1.0 mg/l. ^

Slope estimation in a parametric measurement error model: A simulation study

In regression analysis, covariate measurement error occurs in many applications. The error-prone covariates are often referred to as latent variables. In this proposed study, we extended the study of Chan et al. (2008) on recovering latent slope in a simple regression model to that in a multiple regression model. We presented an approach that applied the Monte Carlo method in the Bayesian framework to the parametric regression model with the measurement error in an explanatory variable. The proposed estimator applied the conditional expectation of latent slope given the observed outcome and surrogate variables in the multiple regression models. A simulation study was presented showing that the method produces estimator that is efficient in the multiple regression model, especially when the measurement error variance of surrogate variable is large.^