Set covering with our eyes closed

Given a universe $U$ of $n$ elements and a weighted collection $\mathscr{S}$ of $m$ subsets of $U$, the universal set cover problem is to a priori map each element $u \in U$ to a set $S(u) \in \mathscr{S}$ containing $u$ such that any set $X{\subseteq U}$ is covered by S(X)=\cup_{u\in XS(u). The aim is to find a mapping such that the cost of $S(X)$ is as close as possible to the optimal set cover cost for $X$. (Such problems are also called oblivious or a priori optimization problems.) Unfortunately, for every universal mapping, the cost of $S(X)$ can be $\Omega(\sqrt{n})$ times larger than optimal if the set $X$ is adversarially chosen. In this paper we study the performance on average, when $X$ is a set of randomly chosen elements from the universe: we show how to efficiently find a universal map whose expected cost is $O(\log mn)$ times the expected optimal cost. In fact, we give a slightly improved analysis and show that this is the best possible. We generalize these ideas to weighted set cover and show similar guarantees to (nonmetric) facility location, where we have to balance the facility opening cost with the cost of connecting clients to the facilities. We show applications of our results to universal multicut and disc-covering problems and show how all these universal mappings give us algorithms for the stochastic online variants of the problems with the same competitive factors

Holomorphic shadows in the eyes of model theory

We define a subset of an almost complex manifold (M,J) to be a holomorphic shadow if it is the image of a J-holomorphic map from a compact complex manifold. Notice that a J-holomorphic curve is a holomorphic shadow, and so is a complex subvariety of a compact complex manifold. We show that under some conditions on an almost complex structure J on a manifold M, the holomorphic shadows in the Cartesian products of (M,J) form a Zariski-type structure. Checking this leads to non-trivial geometric questions and results. We then apply the work of Hrushovski and Zilber on Zariski-type structures. We also restate results of Gromov and McDuff on J-holomorphic curves in symplectic geometry in the language of shadows structures.Comment: Changed and added conten

EquiFACS: the Equine Facial Action Coding System

Although previous studies of horses have investigated their facial expressions in specific contexts, e.g. pain, until now there has been no methodology available that documents all the possible facial movements of the horse and provides a way to record all potential facial configurations. This is essential for an objective description of horse facial expressions across a range of contexts that reflect different emotional states. Facial Action Coding Systems (FACS) provide a systematic methodology of identifying and coding facial expressions on the basis of underlying facial musculature and muscle movement. FACS are anatomically based and document all possible facial movements rather than a configuration of movements associated with a particular situation. Consequently, FACS can be applied as a tool for a wide range of research questions. We developed FACS for the domestic horse (Equus caballus) through anatomical investigation of the underlying musculature and subsequent analysis of naturally occurring behaviour captured on high quality video. Discrete facial movements were identified and described in terms of the underlying muscle contractions, in correspondence with previous FACS systems. The reliability of others to be able to learn this system (EquiFACS) and consistently code behavioural sequences was high—and this included people with no previous experience of horses. A wide range of facial movements were identified, including many that are also seen in primates and other domestic animals (dogs and cats). EquiFACS provides a method that can now be used to document the facial movements associated with different social contexts and thus to address questions relevant to understanding social cognition and comparative psychology, as well as informing current veterinary and animal welfare practices

On Pain of Death

On Pain of Death is a fictional retelling of the story of Sir Pelleas, who, in Thomas Malory’s Le Morte D’Arthur, is depicted as a noble knight with unrequited love for Lady Ettarde. He follows her for weeks, repeatedly declaring his love for her, despite her clear rejections. In rewriting this story, I hope to draw attention to the fact that, by today’s standards, what he is doing is clear-cut stalking. By introducing a character with a periphery perspective, I hope to call into question how “romantic” these stories of unrequited love really are

State and trait characteristics of anterior insula time-varying functional connectivity.

The human anterior insula (aINS) is a topographically organized brain region, in which ventral portions contribute to socio-emotional function through limbic and autonomic connections, whereas the dorsal aINS contributes to cognitive processes through frontal and parietal connections. Open questions remain, however, regarding how aINS connectivity varies over time. We implemented a novel approach combining seed-to-whole-brain sliding-window functional connectivity MRI and k-means clustering to assess time-varying functional connectivity of aINS subregions. We studied three independent large samples of healthy participants and longitudinal datasets to assess inter- and intra-subject stability, and related aINS time-varying functional connectivity profiles to dispositional empathy. We identified four robust aINS time-varying functional connectivity modes that displayed both "state" and "trait" characteristics: while modes featuring connectivity to sensory regions were modulated by eye closure, modes featuring connectivity to higher cognitive and emotional processing regions were stable over time and related to empathy measures