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The scheduling problem is a key class of optimization problems and has various kinds of applications both in practical and theoretical scenarios. In the scheduling problem, probabilistic analysis is a basic tool for investigating…
The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…
We consider a generalisation of the classical coupon collector's problem, in which at each time step a collector either receives a new copy of a randomly chosen coupon, or loses all their previously collected copies of that coupon. We…
Apportionment is the task of assigning resources to entities with different entitlements in a fair manner, and specifically a manner that is as proportional as possible. The best-known application is the assignment of parliamentary seats to…
In this paper we consider a set of origin-destination pairs in a mixed model in which a network embedded in the plane represents an alternative high-speed transportation system, and study a trip covering problem which consists on locating…
In public transport networks disruptions may occur and lead to travel delays. It is thus interesting to determine whether a traveler can be resilient to delays that occur unexpectedly, ensuring that they can reach their destination in time…
We consider a bivariate diffusion process and we study the first passage time of one component through a boundary. We prove that its probability density is the unique solution of a new integral equation and we propose a numerical algorithm…
Disordered systems have grown in importance in the past decades, with similar phenomena manifesting themselves in many different physical systems. Because of the difficulty of the topic, theoretical progress has mostly emerged from…
We review some representative results for first-passage problems involving so-called mortal or evanescent walkers, i.e., walkers with a finite lifetime. The mortality constraint plays a key role in the modeling of many real scenarios, as it…
Text password has served as the most popular method for user authentication so far, and is not likely to be totally replaced in foreseeable future. Password authentication offers several desirable properties (e.g., low-cost, highly…
Automatic passenger counting (APC) in public transportation has been approached with various machine learning and artificial intelligence methods since its introduction in the 1970s. While equivalence testing is becoming more popular than…
The odds theorem and the corresponding solution algorithm (odds algorithm) are tools to solve a wide range of optimal stopping problems. Its generality and tractability have caught much attention. (Google for instance "Bruss odds" to obtain…
Reorganizing bus frequency to cater for the actual travel demand can save the cost of the public transport system significantly. Many, if not all, existing studies formulate this as a bus frequency optimization problem which tries to…
The elapsed time equation is an age-structured model that describes the dynamics of interconnected spiking neurons through the elapsed time since the last discharge, leading to many interesting questions on the evolution of the system from…
We consider fractional wave equations with exponential or arbitrary polynomial nonlinearities. We prove the global well-posedness on the support of the corresponding Gibbs measures. We provide ill-posedness constructions showing that the…
We study the classical occupancy problem from the viewpoint of its embedding Markov chain. We derive new expressions for the probability mass function and (complementary) distribution function in generalized form. Furthermore, we derive a…
Consider a string of $n$ positions, i.e. a discrete string of length $n$. Units of length $k$ are placed at random on this string in such a way that they do not overlap, and as often as possible, i.e. until all spacings between neighboring…
A typical polling system consists of a number of queues, attended by a single server in a fixed order. The vast majority of papers on polling systems focusses on Poisson arrivals, whereas very few results are available for general arrivals.…
We mathematically construct focal lenses for positive-mass particles in Minkowski space. Particles emanating from a point source, refocus with synchronized proper time regardless of initial direction and velocity. Minkowski space offers a…
Bus bunching is a curse of transportation systems such as buses in a loop. Here we present an analytical method to find the number of revolutions before two buses bunch in an idealised system, as a function of the initial distance and the…