Residential location choice modeling is one of the areas in transportation planning that attempts to examine households location search behavior incorporating their trade-offs between housing quality, prices or rents, distance to work and other key factors. This brings up the need to come up with methods to logically allocate credible choice alternatives for individuals.This article attempts to...

We prove that every quadratic plane differential system having an isochronous center commutes with a polynomial differential system.

In this paper, we construct multimodal spectral geometry by finding a pair of closest commuting operators (CCO) to a given pair of Laplacians. The CCOs are jointly diagonalizable and hence have the same eigenbasis. Our construction naturally extends classical data analysis tools based on spectral geometry, such as diffusion maps and spectral clustering. We provide several synthetic and real exa...

This paper exploits the properties of the commute time to develop a graphspectral method for image segmentation. Our starting point is the lazy random walk on the graph, which is determined by the heat-kernel of the graph and can be computed from the spectrum of the graph Laplacian. We characterise the random walk using the commute time between nodes, and show how this quantity may be computed ...

Let A be an Artin group with standard generating set Σ. Tits conjectured that the only relations in A amongst the squares of the generators are the obvious ones, namely that σ2 and τ2 commute whenever σ and τ commute, for σ, τ ∈ Σ. In this paper we prove Tits’ conjecture for all Artin groups. In fact, given a number m(σ) ≥ 2 for each σ ∈ Σ, we show that the elements {T (σ) = σm(σ) : σ ∈ Σ} gene...

Nowadays, many cities or urban areas, say San Francisco Bay Area, started to converge into a divided “working area” “living area” layout, where people commute daily to working area on mornings and commute back on nights. The commute usually depend on few vital highways. For example, the ”working area” could be San Francisco inner city, and living area could be east bay or south bay, and the vit...

INTRODUCTION The prevalence of obesity is higher in rural than in urban areas of the United States, for reasons that are not well understood. We examined correlations between percentage of rural residents, commute times, food retail gap per capita, and body mass index (BMI) among North Carolina residents. METHODS We used 2000 census data to determine each county's percentage of rural resident...

The average commute time in the US is close to 30 minutes each way. In a world where we wouldn’t need to “drive” the car while commuting, what would be the best use of this time? We see autonomous vehicles as an opportunity to help people reach wellness and high productivity levels. After all, commute time is not just moving from point A to point B. It is also about moving from a mindset to ano...