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We introduce a continuous-time quantum walk on an ultrametric space corresponding to the set of p-adic integers and compute its time-averaged probability distribution. It is shown that localization occurs for any location of the ultrametric…
We present CasualGaze, a novel eye-gaze-based target selection technique to support natural and casual eye-gaze input. Unlike existing solutions that require users to keep the eye-gaze center on the target actively, CasualGaze allows users…
Understanding distance metrics in high-dimensional spaces is crucial for various fields such as data analysis, machine learning, and optimization. The Manhattan distance, a fundamental metric in multi-dimensional settings, measures the…
Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…
Although Bayesian methods are robust and principled, their application in practice could be limited since they typically rely on computationally intensive Markov Chain Monte Carlo algorithms for their implementation. One possible solution…
We investigate three aspects of weak* convergence of the $n$-step distributions of random walks on finite volume homogeneous spaces $G/\Gamma$ of semisimple real Lie groups. First, we look into the obvious obstruction to the upgrade from…
Cycling delivers significant public-health and environmental benefits, yet its uptake in cities is often limited by perceived safety. When street environments appear unsafe, individuals are less likely to cycle, making perception a key…
The objects we perceive guide our eye movements when observing real-world dynamic scenes. Yet, gaze shifts and selective attention are critical for perceiving details and refining object boundaries. Object segmentation and gaze behavior…
In this paper we provide a connection between the geometrical properties of a chaotic dynamical system and the distribution of extreme values. We show that the extremes of so-called physical observables are distributed according to the…
Following the gaze of people inside videos is an important signal for understanding people and their actions. In this paper, we present an approach for following gaze across views by predicting where a particular person is looking…
Gait recognition, which refers to the recognition or identification of a person based on their body shape and walking styles, derived from video data captured from a distance, is widely used in crime prevention, forensic identification, and…
The problem of how to estimate diffusion on a graph effectively is of importance both theoretically and practically. In this paper, we make use of two widely studied indices, geodesic distance and mean first-passage time ($MFPT$) for random…
This paper addresses the challenging problem of estimating the general visual attention of people in images. Our proposed method is designed to work across multiple naturalistic social scenarios and provides a full picture of the subject's…
Preference learning methods, such as Reinforcement Learning from Human Feedback (RLHF) and Direct Preference Optimization (DPO), rely on pairwise human judgments, yet little is known about the cognitive processes underlying these judgments.…
There is a widespread assumption that the peak velocities of visually guided saccades in the dark are up to 10~\% slower than those made in the light. Studies that questioned the impact of the surrounding brightness conditions, come to…
We develop a deterministic large-time mechanism yielding Ces{\`a}ro asymptotic observability inequalities from moving localized observations for conservative evolutions. On each observation interval, exact convexification on a compact…
We present an algorithmic and visual grouping of participants and eye-tracking metrics derived from recorded eye-tracking data. Our method utilizes two well-established visualization concepts. First, parallel coordinates are used to provide…
Mobile gaze tracking involves inferring a user's gaze point or direction on a mobile device's screen from facial images captured by the device's front camera. While this technology inspires an increasing number of gaze-interaction…
A hyperbolic space has been shown to be more capable of modeling complex networks than a Euclidean space. This paper proposes an explicit update rule along geodesics in a hyperbolic space. The convergence of our algorithm is theoretically…
Temporal graphs are commonly used to represent time-resolved relations between entities in many natural and artificial systems. Many techniques were devised to investigate the evolution of temporal graphs by comparing their state at…