Related papers: A proof of the lonely runner conjecture

There have been extensive studies of a random walk among a field of immobile traps (or obstacles), where one is interested in the probability of survival as well as the law of the random walk conditioned on its survival up to time $t$. In…

Evaluating joint probabilities of potential outcomes and observed variables, and their linear combinations, is a fundamental challenge in causal inference. This paper addresses the bounding and identification of these probabilities in…

Ball lightning is a very rarely observed phenomenon that makes it extremely difficult to characterize scientifically. Eye-witness accounts of ball lightning that describe many features in common have been variously recorded for centuries.…

We study the disordered quantum walk in one dimension, and obtain the weak limit theorem.

Visualizing the trajectory of multiple runners with videos collected at different points in a race could be useful for sports performance analysis. The videos and the trajectories can also aid in athlete health monitoring. While the runners…

We study the inverse problem of determining a Signorini obstacle from boundary measurements for the isotropic elasticity system. We prove that the obstacle can be uniquely determined by a single measurement of displacement and normal stress…

A self-avoiding walk with small attractive interactions is described here. The existence of the connective constant is established, and the diffusive behavior is proved using the method of the lace expansion.

In this note, we study an obstacle problem for the elastic flow. We prove the local-in-time existence of weak solutions and discuss their relation to classical solutions when additional regularity is obtained. Related results concerning…

This paper presents a {theoretical study} of the problem of verifying linearizability at runtime, where one seeks for a concurrent algorithm for verifying that the current execution of a given concurrent shared object implementation is…

We consider the proportion of generalized visible lattice points in the plane visited by random walkers. Our work concerns the visible lattice points in random walks in three aspects: (1) generalized visibility along curves; (2) one random…

Detecting individual pedestrians in a crowd remains a challenging problem since the pedestrians often gather together and occlude each other in real-world scenarios. In this paper, we first explore how a state-of-the-art pedestrian detector…

We derive an interesting congruence relation motivated by an Indian Olympiad problem. We give three different proofs of the theorem and mention a few interesting related results.

This paper explores goal-directed proof search in first-order multi-modal logic. The key issue is to design a proof system that respects the modularity and locality of assumptions of many modal logics. By forcing ambiguities to be…

Monocular object detection and tracking have improved drastically in recent years, but rely on a key assumption: that objects are visible to the camera. Many offline tracking approaches reason about occluded objects post-hoc, by linking…

We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.

We offer a reader-friendly introduction to the attracting edge problem (also known as the "triangle conjecture") and its most general current solution of Limic and Tarr\`es (2007). Little original research is reported; rather this article…

We give an elementary, self-contained, and purely combinatorial proof of the Rayleigh monotonicity property of graphs.

The paper presents a counterexample to the Hodge conjecture.

The first version of this paper gave another proof of the Kropholler Conjecture, which gives a relative version of Stallings Ends Theorem, following an earlier incorrect proof. It has been pointed out by Sam Shepherd that the the second…

This work investigates the inverse drift problem in the one-dimensional parabolic equation with the final time data. The authors construct an operator first, whose fixed points are the unknown drift, and then apply it to prove the…