Related papers: Marathon pacing and elevation change
We studied simple random-walk models with asymmetric time delays. Stochastic simulations were performed for hyperbolic-tangent fitness functions and to obtain analytical results we approximated them by step functions. A novel behavior has…
The knowledge of transitions between regular, laminar or chaotic behavior is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there…
Consider the circle $C$ of length 1 and a circular arc $A$ of length $\ell\in (0,1)$. It is shown that there exists $k=k(\ell) \in \mathbb{N}$, and a schedule for $k$ runners along the circle with $k$ constant but distinct positive speeds…
Modern foundation models rely heavily on using scaling laws to guide crucial training decisions. Researchers often extrapolate the optimal architecture and hyper parameters settings from smaller training runs by describing the relationship…
The objective of this work is to provide a mathematical analysis on how a Thoroughbred horse should regulate its speed over the course of a race to optimize performance. Because Thoroughbred horses are not capable of running the whole race…
The existing computational models used to estimate motion sickness are incapable of describing the fact that the predictability of motion patterns affects motion sickness. Therefore, the present study proposes a computational model to…
This work presents, the classification of user activities such as Rest, Walk and Run, on the basis of frequency component present in the acceleration data in a wireless sensor network environment. As the frequencies of the above mentioned…
Human movements in the workspace usually have non-negligible relations with air quality parameters (e.g., CO$_2$, PM2.5, and PM10). We establish a system to monitor indoor human mobility with air quality and assess the interrelationship…
Track and field world records have risen and fallen throughout the history of the sport. A recent rash of record-breaking performances has prompted the question: "How good can we get?". This article offers a review of several attempts to…
Under some mild condition, a random walk in the plane is recurrent. In particular each trajectory is dense, and a natural question is how much time one needs to approach a given small neighborhood of the origin. We address this question in…
Re-identifying participants in ultra-distance running competitions can be daunting due to the extensive distances and constantly changing terrain. To overcome these challenges, computer vision techniques have been developed to analyze…
Based on a mathematical simulation which reproduces accurate split and velocity profiles for the 100 and 200 metre sprints, the magnitudes of altitude and mixed wind/altitude-assisted performances as compared to their sea-level equivalents…
A complete overview of the surrounding vehicle environment is important for driver assistance systems and highly autonomous driving. Fusing results of multiple sensor types like camera, radar and lidar is crucial for increasing the…
Human trajectory prediction is typically posed as a zero-shot generalization problem: a predictor is learnt on a dataset of human motion in training scenes, and then deployed on unseen test scenes. While this paradigm has yielded tremendous…
Human motion diffusion models can synthesize action sequences from text, but controlling motion intensity remains challenging. Existing approaches rely on effort-related adverbs, which are ambiguous and fail to capture quantitative aspects…
Suppose that $k$ runners having different constant speeds run laps on a circular track of unit length. The Lonely Runner Conjecture states that, sooner or later, any given runner will be at distance at least $1/k$ from all the other…
Many biological, chemical, and physical systems are underpinned by stochastic transitions between equilibrium states in a potential energy. Here, we consider such transitions in a minimal model with two possible competing pathways, both…
Low speed does not always guarantee safety in off-road driving. For instance, crossing a ditch may be risky at a low speed due to the risk of getting stuck, yet safe at a higher speed with a controlled, accelerated jump. Achieving such…
Biomechanics and human movement research often involves measuring multiple kinematic or kinetic variables regularly throughout a movement, yielding data that present as smooth, multivariate, time-varying curves and are naturally amenable to…
Emergency evacuation of patients from a hospital can be challenging in the event of a fire. Most emergency evacuation studies are based on the assumption that pedestrians are ambulant and can egress by themselves. However, this is often not…