Sharing analysis is used to statically discover data structures which may overlap in object-oriented programs. Using the abstract interpretation framework, we show that sharing analysis greatly benefits from linearity information. A variable is linear in a program state when different field paths starting from it always reach different objects. We propose a graph-based abstract domain which can represent aliasing, linearity, and sharing information and define all the necessary abstract operators for the analysis of a Java-like language.

The charge-coupled devices used in electron microscopy are coated with a scintillating crystal that gives rise to a severe modulation transfer function (MTF). Exact knowledge of the MTF is imperative for a good correspondence between image simulation and experiment. We present a practical method to measure the MTF above the Nyquist frequency from the beam blocker's shadow image. The image processing has been fully automated and the program is made public. The method is successfully tested on three cameras with various beam blocker shapes.

The mosaics of S-cones and the neurons to which they are connected are relatively well characterized, so the S-cone system is a good vehicle for exploring how the sampling of the retinal image controls visual performance. We used an interferometer to measure the grating acuity of the S-cone system in the fovea and at a range of eccentricities out to 20 deg. We also developed a simple model observer that, by assuming only that cone pathways are noisy and that signals are subject to eccentricity-dependent postreceptoral pooling, predicts the measured acuities from the sampling properties of the S-cone mosaic. The amount of pooling required to explain performance is consistent with that suggested by anatomical and physiological measurements.

Linear dynamical systems are widely used in many different fields from engineering to economics. One simple but important class of such systems is called the single-input transfer function model. Suppose that all variables of the system are sampled for a period using a fixed sample rate. The central issue of this paper is the determination of the smallest sampling rate that will yield a sample that will allow the investigator to identify the discrete-time representation of the system. A critical sampling rate exists that will identify the model. This rate, called the Nyquist rate, is twice the highest frequency component of the system. Sampling at a lower rate will result in an identification problem that is serious. The standard assumptions made about the model and the unobserved innovation errors in the model protect the investigators from the identification problem and resulting biases of undersampling. The critical assumption that is needed to identify an undersampled system is that at least one of the exogenous time series be white noise.

Numerical evaluation of compound distributions is one of the central numerical tasks in insurance mathematics. Two widely used techniques are Panjer recursion and transform methods. Many authors have pointed out that aliasing errors imply the need to consider the whole distribution if transform methods are used, a potential drawback especially for heavy-tailed distributions. We investigate the magnitude of aliasing errors and show that this problem can be solved by a suitable change of measure.