Spectral analysis of pair-correlation bandwidth: Application to cell biology images

Images from cell biology experiments often indicate the presence of cell clustering, which can provide insight into the mechanisms driving the collective cell behaviour. Pair-correlation functions provide quantitative information about the presence, or absence, of clustering in a spatial distribution of cells. This is because the pair-correlation function describes the ratio of the abundance of pairs of cells, separated by a particular distance, relative to a randomly distributed reference population. Pair-correlation functions are often presented as a kernel density estimate where the frequency of pairs of objects are grouped using a particular bandwidth (or bin width), Δ>0. The choice of bandwidth has a dramatic impact: choosing Δ too large produces a pair-correlation function that contains insufficient information, whereas choosing Δ too small produces a pair-correlation signal dominated by fluctuations. Presently, there is little guidance available regarding how to make an objective choice of Δ. We present a new technique to choose Δ by analysing the power spectrum of the discrete Fourier transform of the pair-correlation function. Using synthetic simulation data, we confirm that our approach allows us to objectively choose Δ such that the appropriately binned pair-correlation function captures known features in uniform and clustered synthetic images. We also apply our technique to images from two different cell biology assays. The first assay corresponds to an approximately uniform distribution of cells, while the second assay involves a time series of images of a cell population which forms aggregates over time. The appropriately binned pair-correlation function allows us to make quantitative inferences about the average aggregate size, as well as quantifying how the average aggregate size changes with time.

Power system stability implications from electromechanical wave propagation

Electromechanical wave propagation characterizes the first-swing dynamic response in a spatially delayed manner. This paper investigates the characteristics of this phenomenon in two-dimensional and one-dimensional power systems. In 2-D systems, the wave front expands as a ripple in a pond. In 1-D systems, the wave front is more concentrated, retains most of its magnitude, and travels like a pulse on a string. This large wave front is more impactful upon any weak link and easily causes transient instability in 1-D systems. The initial disturbance injects both high and low frequency components, but the lumped nature of realistic systems only permits the lower frequency components to propagate through. The kinetic energy split at a junction is equal to the generator inertia ratio in each branch in an idealized continuum system. This prediction is approximately valid in a realistic power system. These insights can enhance understanding and control of the traveling waves.

Application of inverse filtering technique in power system studies

This paper demonstrates the application of inverse filtering technique for power systems. In order to implement this method, the control objective should be based on a system variable that needs to be set on a specific value for each sampling time. A control input is calculated to generate the desired output of the plant and the relationship between the two is used design an auto-regressive model. The auto-regressive model is converted to a moving average model to calculate the control input based on the future values of the desired output. Therefore, required future values to construct the output are predicted to generate the appropriate control input for the next sampling time.