Reliance on metrics is a fundamental challenge for AI.

Through a series of case studies, we review how the unthinking pursuit of metric optimization can lead to real-world harms, including recommendation systems promoting radicalization, well-loved teachers fired by an algorithm, and essay grading software that rewards sophisticated garbage. The metrics used are often proxies for underlying, unmeasurable quantities (e.g., "watch time" of a video as a proxy for "user satisfaction"). We propose an evidence-based framework to mitigate such harms by (1) using a slate of metrics to get a fuller and more nuanced picture; (2) conducting external algorithmic audits; (3) combining metrics with qualitative accounts; and (4) involving a range of stakeholders, including those who will be most impacted.

Differential cell counts using center-point networks achieves human-level accuracy and efficiency over segmentation.

Differential cell counts is a challenging task when applying computer vision algorithms to pathology. Existing approaches to train cell recognition require high availability of multi-class segmentation and/or bounding box annotations and suffer in performance when objects are tightly clustered. We present differential count network ("DCNet"), an annotation efficient modality that utilises keypoint detection to locate in brightfield images the centre points of cells (not nuclei) and their cell class. The single centre point annotation for DCNet lowered burden for experts to generate ground truth data by 77.1% compared to bounding box labeling. Yet centre point annotation still enabled high accuracy when training DCNet on a multi-class algorithm on whole cell features, matching human experts in all 5 object classes in average precision and outperforming humans in consistency. The efficacy and efficiency of the DCNet end-to-end system represents a significant progress toward an open source, fully computationally approach to differential cell count based diagnosis that can be adapted to any pathology need.

Stability of ring patterns arising from two-dimensional particle interactions.

Pairwise particle interactions arise in diverse physical systems ranging from insect swarms to self-assembly of nanoparticles. In the presence of long-range attraction and short-range repulsion, such systems can exhibit bound states. We use linear stability analysis of a ring equilibrium to classify the morphology of patterns in two dimensions. Conditions are identified that assure the well-posedness of the ring. In addition, weakly nonlinear theory and numerical simulations demonstrate how a ring can bifurcate to more complex equilibria including triangular shapes, annuli, and spot patterns with N-fold symmetry. Many of these patterns have been observed in nature, although a general theory has been lacking, in particular how small changes to the interaction potential can lead to large changes in the self-organized state.

A mathematical model of a crocodilian population using delay-differential equations.

The crocodilia have multiple interesting characteristics that affect their population dynamics. They are among several reptile species which exhibit temperature-dependent sex determination (TSD) in which the temperature of egg incubation determines the sex of the hatchlings. Their life parameters, specifically birth and death rates, exhibit strong age-dependence. We develop delay-differential equation (DDE) models describing the evolution of a crocodilian population. In using the delay formulation, we are able to account for both the TSD and the age-dependence of the life parameters while maintaining some analytical tractability. In our single-delay model we also find an equilibrium point and prove its local asymptotic stability. We numerically solve the different models and investigate the effects of multiple delays on the age structure of the population as well as the sex ratio of the population. For all models we obtain very strong agreement with the age structure of crocodilian population data as reported in Smith and Webb (Aust. Wild. Res. 12, 541-554, 1985). We also obtain reasonable values for the sex ratio of the simulated population.

Vorticity dynamics and sound generation in two-dimensional fluid flow.

An approximate solution to the two-dimensional incompressible fluid equations is constructed by expanding the vorticity field in a series of derivatives of a Gaussian vortex. The expansion is used to analyze the motion of a corotating Gaussian vortex pair, and the spatial rotation frequency of the vortex pair is derived directly from the fluid vorticity equation. The resulting rotation frequency includes the effects of finite vortex core size and viscosity and reduces, in the appropriate limit, to the rotation frequency of the Kirchhoff point vortex theory. The expansion is then used in the low Mach number Lighthill equation to derive the far-field acoustic pressure generated by the Gaussian vortex pair. This pressure amplitude is compared with that of a previous fully numerical simulation in which the Reynolds number is large and the vortex core size is significant compared to the vortex separation. The present analytic result for the far-field acoustic pressure is shown to be substantially more accurate than previous theoretical predictions. The given example suggests that the vorticity expansion is a useful tool for the prediction of sound generated by a general distributed vorticity field.