A Framework for Program Development Based on Schematic Proof

Often, calculi for manipulating and reasoning about programs can be recast as calculi for synthesizing programs. The difference involves often only a slight shift of perspective: admitting metavariables into proofs. We propose that such calculi should be implemented in logical frameworks that support this kind of proof construction and that such an implementation can unify program verification and synthesis. Our proposal is illustrated with a worked example developed in Paulson's Isabelle system. We also give examples of existent calculi that are closely related to the methodology we are proposing and others that can be profitably recast using our approach

Human Ipsilateral Motor Physiology and Neuroprosthetic Applications in Chronic Stroke

Improving the recovery of lost motor function in hemiplegic chronic stroke survivors is a critical need to improve the lives of these patients. Over the last several decades, neuroprosthetic systems have emerged as novel tools with the potential to restore function in a variety of patient populations. While traditional neuroprosthetics have focused on using neural activity contralateral to a moving limb for device control, an alternative control signal may be necessary to develop brain-computer interface (BCI) systems in stroke survivors that suffer damage to the cortical hemisphere contralateral to the affected limb. While movement-related neural activity also occurs in the hemisphere ipsilateral to a moving limb, it is uncertain if these signals can be used within BCI systems. This dissertation examines the motor activity ipsilateral to a moving limb and the potential use of these signals for neuroprosthetic applications in chronic stroke survivors. Patients performed three-dimensional (3D) reaching movements with the arm ipsilateral to an electrocorticography (ECoG) array in order to assess the extent of kinematic information that can be decoded from the cortex ipsilateral to a moving limb. Additionally, patients performed the same task with the arm contralateral to the same ECoG arrays, allowing us to compare the neural representations of contralateral and ipsilateral limb movements. While spectral power changes related to ipsilateral arm movements begin later and are lower in amplitude than power changes related to contralateral arm movements, 3D kinematics from both contralateral and ipsilateral arm trajectories can be decoded with similar accuracies. The ability to decode movement kinematics from the ipsilateral cortical hemisphere demonstrates the potential to use these signals within BCI applications for controlling multiple degrees of freedom. Next we examined the relationship between electrode invasiveness and signal quality. The ability to decode movement kinematics from neural activity was significantly decreased in simulated electroencephalography (EEG) signals relative to ECoG signals, indicating that invasive signals would be necessary to implement BCI systems with multiple degrees of freedom. For ECoG signals, the human dura also causes a significant decrease in signal quality when electrodes with small spatial sizes are used. This tradeoff between signal quality and electrode invasiveness should therefore be taken into account when designing ECoG BCI systems. Finally, chronic stroke survivors used activity associated with affected hand motor intentions, recorded from their unaffected hemisphere using EEG, to control simple BCI systems. This demonstrates that motor signals from the ipsilateral hemisphere are viable for BCI applications, not only in motor-intact patients, but also in chronic stroke survivors. Taken together, these experiments provide initial demonstrations that it is possible to develop BCI systems using the unaffected hemisphere in stroke survivors with multiple degrees of freedom. Further development of these BCI systems may eventually lead to improving function for a significant population of patients

The Stripe 82 Massive Galaxy Project III: A Lack of Growth Among Massive Galaxies

The average stellar mass (Mstar) of high-mass galaxies (Mstar > 3e11 Msun) is expected to grow by ~30% since z~1, largely through ongoing mergers that are also invoked to explain the observed increase in galaxy sizes. Direct evidence for the corresponding growth in stellar mass has been elusive, however, in part because the volumes sampled by previous redshift surveys have been too small to yield reliable statistics. In this work, we make use of the Stripe 82 Massive Galaxy Catalog to build a mass-limited sample of 41,770 galaxies (Mstar > 1.6e11) with optical to near-IR photometry and a large fraction (>55%) of spectroscopic redshifts. Our sample spans 139 square degrees, significantly larger than most previous efforts. After accounting for a number of potential systematic errors, including the effects of Mstar scatter, we measure galaxy stellar mass functions over 0.3 < z < 0.65 and detect no growth in the typical Mstar of massive galaxies with an uncertainty of 9%. This confidence level is dominated by uncertainties in the star formation history assumed for Mstar estimates, although our inability to characterize low surface-brightness outskirts may be the most important limitation of our study. Even among these high-mass galaxies, we find evidence for differential evolution when splitting the sample by recent star formation (SF) activity. While low-SF systems appear to become completely passive, we find a mostly sub-dominant population of galaxies with residual, but low rates of star formation (~1 Msun/yr) number density does not evolve. Interestingly, these galaxies become more prominent at higher Mstar, representing ~10% of all galaxies at Mstar ~ 1e12 Msun and perhaps dominating at even larger masses.Comment: Accepted in Ap