The lonely runner with seven runners

Suppose $k+1$ runners having nonzero constant speeds run laps on a unit-length circular track starting at the same time and place. A runner is said to be lonely if she is at distance at least $1/(k+1)$ along the track to every other runner. The lonely runner conjecture states that every runner gets lonely. The conjecture has been proved up to six runners ($k\le 5$). A formulation of the problem is related to the regular chromatic number of distance graphs. We use a new tool developed in this context to solve the first open case of the conjecture with seven runners

Lonely runners in function fields

The lonely runner conjecture, now over fifty years old, concerns the following problem. On a unit length circular track, consider $m$ runners starting at the same time and place, each runner having a different constant speed. The conjecture asserts that each runner is lonely at some point in time, meaning distance at least $1/m$ from the others. We formulate a function field analogue, and give a positive answer in some cases in the new setting

Body Image in Long Distance Runners

In lieu of an abstract, below is the essay\u27s first paragraph. How would you describe the ideal runner’s body? Would you say it is tall or short? Skinny or fat? Muscular or lean? Is it the same as society’s ideal female’s body? A Division 2 collegiate female distance runner recently stated, “The ideal runner’s body is having a six pack and muscular quads and an overall skinny physique. The ideal female body, from what I gather from society, is having larger breasts and a butt, nice hair and a nice face. Runners do not always have the biggest extremities, so that makes me feel more self-conscious about my body because I definitely look and feel like a distance runner.” This runner’s response is just one of the many examples of how there is a conflict between what it means to want an ideal runner’s body, and the value of it for competing in the sport verses the reality of the American societal ideal

DeepPicar: A Low-cost Deep Neural Network-based Autonomous Car

We present DeepPicar, a low-cost deep neural network based autonomous car platform. DeepPicar is a small scale replication of a real self-driving car called DAVE-2 by NVIDIA. DAVE-2 uses a deep convolutional neural network (CNN), which takes images from a front-facing camera as input and produces car steering angles as output. DeepPicar uses the same network architecture---9 layers, 27 million connections and 250K parameters---and can drive itself in real-time using a web camera and a Raspberry Pi 3 quad-core platform. Using DeepPicar, we analyze the Pi 3's computing capabilities to support end-to-end deep learning based real-time control of autonomous vehicles. We also systematically compare other contemporary embedded computing platforms using the DeepPicar's CNN-based real-time control workload. We find that all tested platforms, including the Pi 3, are capable of supporting the CNN-based real-time control, from 20 Hz up to 100 Hz, depending on hardware platform. However, we find that shared resource contention remains an important issue that must be considered in applying CNN models on shared memory based embedded computing platforms; we observe up to 11.6X execution time increase in the CNN based control loop due to shared resource contention. To protect the CNN workload, we also evaluate state-of-the-art cache partitioning and memory bandwidth throttling techniques on the Pi 3. We find that cache partitioning is ineffective, while memory bandwidth throttling is an effective solution.Comment: To be published as a conference paper at RTCSA 201

The Cowl - v.33 - n.8 - 1970-71 Winter Sports Special - Dec 02, 1970

The Cowl - student newspaper of Providence College. Volume 33 No. 8, Winter Sports Special \u2770-71 - December 2, 1970. 12 pages

Racing against time? Aspects of the temporal organization of the runner's world

Drawing on documentary sources and participant observation, I seek to specify salient temporal characteristics of the social world of running. Extant analyses seem preoccupied with criticizing running temporality for reproducing, in a sporting context, those Taylorized, alienating beliefs and oppressive practices typical of capitalist sites of production. A different point of departure, runners' own understandings, shows that temporal considerations are a key constituent of the runner's self that is not experienced as alienated. Three aspects of running temporality are highlighted: the large-scale temporal organization of the running world, with a focus on the cyclical racing pattern and the planned and scheduled character of training; temporal features of running careers; and the way in which "times" figure in the activity of running and its description. I conclude that these temporal organizations are important symbolic resources that help to build and reaffirm the runner's self. Rather than time alienating and exploiting runners, runners exploit it as a constructive resource that they can deploy in diverse ways

Optimal Pacing for Running 400 m and 800 m Track Races

Physicists seeking to understand complex biological systems often find it rewarding to create simple "toy models" that reproduce system behavior. Here a toy model is used to understand a puzzling phenomenon from the sport of track and field. Races are almost always won, and records set, in 400 m and 800 m running events by people who run the first half of the race faster than the second half, which is not true of shorter races, nor of longer. There is general agreement that performance in the 400 m and 800 m is limited somehow by the amount of anaerobic metabolism that can be tolerated in the working muscles in the legs. A toy model of anaerobic metabolism is presented, from which an optimal pacing strategy is analytically calculated via the Euler-Lagrange equation. This optimal strategy is then modified to account for the fact that the runner starts the race from rest; this modification is shown to result in the best possible outcome by use of an elementary variational technique that supplements what is found in undergraduate textbooks. The toy model reproduces the pacing strategies of elite 400 m and 800 m runners better than existing models do. The toy model also gives some insight into training strategies that improve performance.Comment: 14 pages, 4 figures, submitted to the American Journal of Physic