This article analyzes the ambitious Case Quality Assessment System (CQAS) that the Supreme People’s Court of China (SPC) promoted during the first half of the 2010s. It offers a case-study of Court J, a grassroots court located in an affluent urban metropolis of China that struggled to come out ahead in the CQAS competition. The article discusses how the SPC quantified judging and the problems created by the metricization process. The CQAS project is analyzed as a case of metric fixation. By identifying the problems that doomed the CQAS, the article points out the challenges facing the authoritarian regime in subjecting good judging to quantitative output standards. The CQAS is a metric that judges judging. It reveals how judging is viewed by the party-state. The article concludes by discussing the legacy of the CQAS. Though it nominally ended in 2014, key indicators that it introduced for supervising judges are still used by the Chinese courts today. The CQAS presaged the growing centralization that the Chinese judicial system is undergoing today. Though the SPC has terminated the tournament-style competition that defined the CQAS, the metric remains the template used to evaluate judging.

In order to prevent robot manipulators from reaching singularities, the “distance” from the current configuration to a singular configuration should be measured. This paper presents a novel metric based on geometric average normalized volume spanned by weighted screws to measure closeness to singularities for both serial and parallel manipulators. The weighted screws are proposed to reinterpret the physical meaning of twists and wrenches, so the problem of inconsistent dimensions in the dot product of screws has been eliminated. Compared with other existing methods, the proposed metric can obtain an identical result for similar manipulators with different sizes. Furthermore, the metric is independent of the selection of base screws, which is very suitable for the overconstrained or lower mobility parallel manipulator whose base screws are not uniquely definite. Besides, the geometrical meaning of the metric is related to the dimensionless volume of a high dimensional polyhedron, and hence the metric is insensitive to screw magnitude.

When reviewing the various fish-based community indicators aiming at assessing the ecological status of marine communities and/or ecosystems, a typology consisting of three major components emerges. The first component highlights the choice of relevant metrics associated with a level of organization (e.g. population or community). The second relies on the method used to combine the metrics (an aggregated indicator or a synoptic table). The third refers to the type of analysis (direct or indirect) that is used to establish the link between the metrics and a given pressure. In this paper we use the Vilaine coastal-estuarine fish communities as a case study to discuss and relate two different approaches to the suggested typology. The first approach (time-trend approach) is based on historical series of data, whereas the second approach (multi-metric index, MMI) is based on a geographic series including various French estuaries. They were developed or adapted from French studies but are representative of the approaches used in Europe. When applied to the case study, they differed in their diagnosis: the time-trend approach indicated that the bay of Vilaine habitat was deteriorating, whereas the MMI, which compares many French estuaries, indicated a good environmental state. Differences and complementarities between the approaches are thoroughly discussed with respect to the three mains components of the typology. This work appears at a particular moment, when several fish-based indicators are being developed in France and the rest of Europe. It intends to serve as an element of the ongoing reflection concerning the limitations of the various approaches that can be used to develop such indicators.

In this note we consider a stability property of p-harmonic functions in general metric measure spaces. Despite the fact that there may not be a corresponding differential equation, it is shown here that a family of uniformly convergent p-harmonic functions converges to a p-harmonic function; that is, the collection of p-harmonic functions forms a closed subspace in a certain Ho¨lder class. As a consequence, it is shown that a family of p-harmonic functions bounded in a Sobolev-type space (called the Newtonian space) has a sequence that converges locally uniformly in the domain of harmonicity to a p-harmonic function. This result is used to construct p-harmonic functions on unbounded domains. We also use this convergence result to prove a characterization of a parabolicity property of metric measure spaces. This characterization has been given for Riemannian manifolds by Holopainen, and the result here is a generalization of Holopainen's result.

Intrinsic volumes are key functionals in convex geometry and have also appeared in several stochastic settings. Here we relate them to questions of regularity in Gaussian processes with regard to Itô–Nisio oscillation and metrization of GB/GC indexing sets. Various bounds and estimates are presented, and questions for further investigation are suggested. From alternate points of view, much of the discussion can be interpreted in terms of (i) random sets and (ii) properties of (deterministic) infinite-dimensional convex bodies.

We derive conditions for the time-uniform continuity of random sequences with respect to variations of governing parameters, and also obtain some estimates of the modulus of continuity. We then apply the results to find conditions of continuity for Markov chains with arbitrary state space, and to construct finite approximations to them.