arXiv research

Model shows rational agents are eliminated by competition, leaving irrational players.

Study tiling spaces over irrational tori using diffeological classification.

Modeling stock price adjustments due to irrational agent behavior.

Study the stable norm on irrational slopes of 2-torus.

We describe Veech groups of flat surfaces arising from irrational angled polygonal billiards or irreducible stable abelian differentials. For irrational polygonal billiards, we prove that these groups are non-discrete subgroups of SO(2,R) and we calculate their rank.

Study noncommutative coverings of irrational quantum tori.

Study irrational pencils on complex manifolds, finding non-finitely generated homology.

Review of conformal geometry in irrational rotation algebra.

Study symplectic and Hamiltonian actions on irrational ruled surfaces, proving existence and non-existence of extensions.

We show that the Novikov-Shubin invariant of an element of the integral group ring of the lamplighter group Z_2 \wr Z can be irrational. This disproves a conjecture of Lott and Lueck. Furthermore we show that every positive real number is equal to the Novikov-Shubin invariant of some element of the real group ring of Z…

Study irrational rotations and construct 2-filling rays on infinite type surfaces.

We prove that there are examples of finitely generated groups G together with group ring elements Q \in \bbQ G for which the von Neumann dimension \dim_{LG}\ker Q is irrational, so (in conjunction with other known results) answering a question of Atiyah.

We give examples of finitely presented groups containing elements with irrational (in fact, transcendental) stable commutator length, thus answering in the negative a question of M. Gromov. Our examples come from 1-dimensional dynamics, and are related to the generalized Thompson groups studied by M. Stein, I. Liousse …

New coefficient detects irrational rotation behavior on infinite-type surfaces.

Estimates dimensions of maximal simplices for rational and irrational trees in Outer space.

In this paper, we prove that on every Finsler $n$-sphere $(S^n, F)$ for $n\ge 6$ with reversibility $λ$ and flag curvature $K$ satisfying $(\fracλ{λ+1})^2<K\le 1$, either there exist infinitely many prime closed geodesics or there exist $[\frac{n}{2}]-2$ closed geodesics possessing irrational average indices. If in add…

We study the geometry of the Margulis region associated with an irrational screw translation $g$ acting on the 4-dimensional real hyperbolic space. This is an invariant domain with the parabolic fixed point of $g$ on its boundary which plays the role of an invariant horoball for a translation in dimensions $\leq 3$. Th…

Modeling preference rankings with salient features to explain irrational choices.

This paper uses hyperbolic geometry to prove Markov's theorem on irrational numbers and quadratic forms.

Standard economic theory assumes that agents in markets behave rationally. However, the observation of extremely large fluctuations in the price of financial assets that are not correlated to changes in their fundamental value, as well as the extreme instance of financial bubbles and crashes, imply that markets (at lea…

Given a discrete subgroup of the isometries of n-dimensional hyperbolic space there is always a region kept precisely invariant under the stabilizer of a parabolic fixed point, called the Margulis region. While in dimensions 2 and 3 this region is a horoball, it has in general a more complicated shape due to the existe…

Proposes a generic prediction architecture for autonomous vehicles considering both rational and irrational driving behaviors.

In this paper, we present a multi-period trading model by assuming that traders face not only asymmetric information but also heterogenous prior beliefs, under the requirement that the insider publicly disclose his stock trades after the fact. We show that there is an equilibrium in which the irrational insider camoufl…

Improved model better fits financial data.

Researchers calculate Morse index and nullity for two specific minimal hypersurfaces.

New trekking approach reduces collisions in multi-player bandits.

A policy for near-optimal multi-player bandits with non-zero collision rewards.

A multi-player bandit system resists adversarial attacks with near-optimal regret.

Discrete-time games reveal payoffs after both players stop, leading to new equilibrium strategies.

Predict player lifetime value based on engagement metrics.

New algorithm reduces regret in multi-player bandits with collision information.

Paper proposes player roles from match data to help clubs.

New algorithms for n-player games using a player-centered approach.

New algorithm for multi-player bandits with selfish players, achieving logarithmic regret.

Symmetric game analysis shows Nash equilibria in three strategic states.

We develop a machine learning approach to represent and analyze the underlying spatial structure that governs shot selection among professional basketball players in the NBA. Typically, NBA players are discussed and compared in an heuristic, imprecise manner that relies on unmeasured intuitions about player behavior. T…

Paper uses Apprenticeship Learning to model player behavior in interactive narratives.

New algorithm for multi-player bandits in changing environments.

New algorithm tackles multi-player bandit problems with limited access to arms.

Paper presents Transfer Portal model for accurate player performance predictions.

A new algorithm RESYNC for defenders against malicious attackers in multi-player bandits.

Study predicts soccer player market values using machine learning and SHAP for interpretability.

Algorithm optimizes multi-player learning with noisy rewards without direct communication.

Paper introduces new metrics for evaluating player actions in soccer.

New strategy achieves optimal regret without communication or collisions in multi-player bandit.

New algorithm for multi-player bandits in decentralized, asynchronous systems.

Different models to study the wealth distribution in an artificial society have considered a transactional dynamics as the driving force. Those models include a risk aversion factor, but also a finite probability of favoring the poorer agent in a transaction. Here we study the case where the partners in the transaction…

Paper uses DRL to evaluate NHL players based on game context.