Related papers: Parking and the visual perception of space

During the attempt to line up into a dense traffic people have necessarily to share a limited space under turbulent conditions. From the statistical point view it generally leads to a probability distribution of the distances between the…

We investigate the occupancy statistics of birds on a wire and on higher-dimensional substrates. In one dimension, birds land one by one on a wire and rest where they land. Whenever a newly arriving bird lands within a fixed distance of…

It has been demonstrated many times that the behavior of the human visual system is connected to the statistics of natural images. Since machine learning relies on the statistics of training data as well, the above connection has…

We show that the spacing distribution between parked cars can be obtained as a solution of certain linear distributional fixed point equation. The results are compared with the data measured on the streets of Hradec Kralove. We also discuss…

For pattern recognition like image recognition, it has become clear that each machine-learning dictionary data actually became data in probability space belonging to Euclidean space. However, the distances in the Euclidean space and the…

Bird flocking is a striking example of collective animal behaviour. A vivid illustration of this phenomenon is provided by the aerial display of vast flocks of starlings gathering at dusk over the roost and swirling with extraordinary…

We illustrate the experimental, empirical, approach to mathematics (that contrary to popular belief, is often rigorous), by using parking functions and their "area" statistic, as a case study. Our methods are purely finitistic and…

In a scenario of growing usage of park-and-ride facilities, understanding and predicting car park occupancy is becoming increasingly important. This study presents a model that effectively captures the occupancy patterns of park-and-ride…

We have carried out car-following experiments with a 25-car-platoon on an open road section to study the relation between a car's speed and its spacing under various traffic conditions, in the hope to resolve a controversy surrounding this…

Smart cities around the world have begun monitoring parking areas in order to estimate available parking spots and help drivers looking for parking. The current results are promising, indeed. However, existing approaches are limited by the…

Studies using massive, passively data collected from communication technologies have revealed many ubiquitous aspects of social networks, helping us understand and model social media, information diffusion, and organizational dynamics. More…

We consider machine learning in a comparison-based setting where we are given a set of points in a metric space, but we have no access to the actual distances between the points. Instead, we can only ask an oracle whether the distance…

Measuring the distance between data points is fundamental to many statistical techniques, such as dimension reduction or clustering algorithms. However, improvements in data collection technologies has led to a growing versatility of…

In this paper we present new results on the enumeration of parking functions and labeled forests. We introduce new statistics on parking functions, which are then extended to labeled forests via bijective correspondences. We determine the…

Transportation distance information is a powerful resource, but location records are often censored due to privacy concerns or regulatory mandates. We outline methods to approximate, sample from, and compare distributions of distances…

We extend the notion of parking functions to parking sequences, which include cars of different sizes, and prove a product formula for the number of such sequences.

Numerical models indicate that collective animal behaviour may emerge from simple local rules of interaction among the individuals. However, very little is known about the nature of such interaction, so that models and theories mostly rely…

Automated capture of animal pose is transforming how we study neuroscience and social behavior. Movements carry important social cues, but current methods are not able to robustly estimate pose and shape of animals, particularly for social…

During the attempt to park a car in the city the drivers have to share limited resources (the available roadside). We show that this fact leads to a predictable distribution of the distances between the cars that depends on the length of…

Certain concepts, words, and images are intuitively more similar than others (dog vs. cat, dog vs. spoon), though quantifying such similarity is notoriously difficult. Indeed, this kind of computation is likely a critical part of learning…