Related papers: Balls-in-bins models with asymmetric feedback and …
Consider sequential packing of unit balls in a large cube, as in the Renyi car-parking model, but in any dimension and with Poisson input. We show after suitable rescaling that the spatial distribution of packed balls tends to that of a…
The objective of this study was to incorporate contextual information into the modelling of player movements. This was achieved by combining the distributions of forthcoming passing contests that players committed to and those they did not.…
This article is devoted to the stabilization of two underactuated planar systems, the well-known straight beam-and-ball system and an original circular beam-and-ball system. The feedback control for each system is designed, using the Jordan…
Abelian sandpile models, both deterministic, such as the Bak, Tang, Wiesenfeld (BTW) model [P. Bak, C. Tang and K. Wiesenfeld, Phys. Rev. Lett. {\bf 59}, 381 (1987)], and stochastic, such as the Manna model [S.S. Manna, J. Phys. A {\bf 24},…
The box-ball system (BBS), introduced by Takahashi and Satsuma in 1990, is a cellular automaton that exhibits solitonic behaviour. In this article, we study the BBS when started from a random two-sided infinite particle configuration. For…
Deep models trained through maximum likelihood have achieved state-of-the-art results for survival analysis. Despite this training scheme, practitioners evaluate models under other criteria, such as binary classification losses at a chosen…
Suppose one buys two very similar stocks and is curious about how much, after some time T, one of them will contribute to the overall asset, expecting, of course, that it should be around 1/2 of the sum. Here we examine this question within…
We introduce a family of two-dimensional reflected random walks in the positive quadrant and study their Martin boundary. While the minimal boundary is systematically equal to a union of two points, the full Martin boundary exhibits an…
Traditionally Bayesian decision-theoretic design of experiments proceeds by choosing a design to minimise expectation of a given loss function over the space of all designs. The loss function encapsulates the aim of the experiment, and the…
Inspired by the Japanese game Pachinko, we study simple (perfectly "inelastic" collisions) dynamics of a unit ball falling amidst point obstacles (pins) in the plane. A classic example is that a checkerboard grid of pins produces the…
We consider the allocation problem in which $m \leq (1-\epsilon) dn $ items are to be allocated to $n$ bins with capacity $d$. The items $x_1,x_2,\ldots,x_m$ arrive sequentially and when item $x_i$ arrives it is given two possible bin…
Estimating win probability is one of the classic modeling tasks of sports analytics. Many widely used win probability estimators use machine learning to fit the relationship between a binary win/loss outcome variable and certain game-state…
Animals move smoothly and reliably in unpredictable environments. Models of sensorimotor control have assumed that sensory information from the environment leads to actions, which then act back on the environment, creating a single,…
Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…
Following a long tradition of physicists who have noticed that the Ising model provides a general background to build realistic models of social interactions, we study a model of financial price dynamics resulting from the collective…
We establish empirical bounds on behavioral inference through controlled experiments at scale: LLM-based agents assigned one of 36 behavioral profiles (9 belief systems x 4 motivations) generate over 1.5 million behavioral sequences across…
A mode, or `most likely point', for a probability measure $\mu$ can be defined in various ways via the asymptotic behaviour of the $\mu$-mass of balls as their radius tends to zero. Such points are of intrinsic interest in the local theory…
Spin systems with hyperbolic symmetry originated as simplified models for the Anderson metal--insulator transition, and were subsequently found to exactly describe probabilistic models of linearly reinforced walks and random forests. In…
We propose a new model for forming beliefs and learning about unknown probabilities (such as the probability of picking a red marble from a bag with an unknown distribution of coloured marbles). The most widespread model for such situations…
We extend a general result showing that the asymptotic behavior of high moments, factorial or standard, of random variables, determines the asymptotically normality, from the one dimensional to the multidimensional setting. This approach…