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Psychometrics and quantitative psychology rely strongly on statistical models to measure psychological processes. As a branch of mathematics, geometry is inherently connected to measurement and focuses on properties such as distance and…

We introduce a conceptual framework that associates syntax and semantics with vertical and horizontal directions in principal bundles and related constructions. This notion of geometry corresponds to a mechanism for performing goal-directed…

Computer graphics seeks to deliver compelling images, generated within a computing budget, targeted at a specific display device, and ultimately viewed by an individual user. The foveated nature of human vision offers an opportunity to…

A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete…

Goal-oriented navigation presents a fundamental challenge for autonomous systems, requiring agents to navigate complex environments to reach designated targets. This survey offers a comprehensive analysis of multimodal navigation approaches…

Vision-Language Models (VLMs) have demonstrated remarkable performance across a variety of real-world tasks. However, existing VLMs typically process visual information by serializing images, a method that diverges significantly from the…

The perception-related origins of physical measures and standards are considered within the framework of the general observer theory. The impact of observer characteristics on the development of observer-centric physics, physical concepts…

Research in cognitive science has provided extensive evidence of human cognitive ability in performing physical reasoning of objects from noisy perceptual inputs. Such a cognitive ability is commonly known as intuitive physics. With…

A central goal of neuroscience is to understand the representations formed by brain activity patterns and their connection to behavior. The classical approach is to investigate how individual neurons encode the stimuli and how their tuning…

In this thesis we address two related aspects of visual object recognition: the use of motion information, and the use of internal supervision, to help unsupervised learning. These two aspects are inter-related in the current study, since…

Human visual perception carves a scene at its physical joints, decomposing the world into objects, which are selectively attended, tracked, and predicted as we engage our surroundings. Object representations emancipate perception from the…

Topological data analysis asks when balls in a metric space $(X,d)$ intersect. Geometric data analysis asks how much balls have to be enlarged to intersect. We connect this principle to the traditional core geometric concept of curvature.…

A pedagogical but concise overview of Riemannian geometry is provided, in the context of usage in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions,…

In this paper, we propose that 'embodied mathematics' should be studied not only by reduction to the present individual bodily experience but in an historical context as well, as far as the origins of mathematics are concerned. Some early…

Cities are systems with a large number of constituents and agents interacting with each other and can be considered as emblematic of complex systems. Modeling these systems is a real challenge and triggered the interest of many disciplines…

The purpose of this contribution is to give an introduction to quantum geometry and loop quantum gravity for a wide audience of both physicists and mathematicians. From a physical point of view the emphasis will be on conceptual issues…

This paper lays the foundations for a unified framework for numerically and computationally applying methods drawn from a range of currently distinct geometrical approaches to statistical modelling. In so doing, it extends information…

General Relativity describes gravity in geometrical terms. This suggests that quantizing such theory is the same as quantizing geometry. The subject can therefore be called quantum geometry and one may think that mathematicians are…

Perception of the visually disjoint surfaces of our cluttered world as whole objects, physically distinct from those overlapping them, is a cognitive phenomenon called objectness that forms the basis of our visual perception. Shared by all…

The notion of optical geometry, introduced more than twenty years ago as a formal tool in quantum field theory on a static background, has recently found several applications to the study of physical processes around compact objects. In…