The sensing power of vehicle fleets

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Monitoring urban environments is a challenging task; air pollution, road quality, congestion, and other quantities of interest vary widely across both time and space, requiring much effort to accurately monitor. In this PNAS paper we show attaching sensors to third party urban vehicles – like cars, taxis, buses or trucks – could offer a cheap and scalable solution to this problem. See this video and this visualization for more info.

                   

The curious tourist problem

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A puzzle for probability theorists:

A curious tourist arrives in a city with N roads arranged in a network G. She decides to explore the city by taking taxis to randomly chosen locations (via shortest paths). After being dropped off by a taxi at a given location, she is immediately picked up by another taxi and brought to a new location. How long does it take her to cover every road at least once? (Code available here.)

In this Physica A paper, we numerically explore the curious tourist problem (and other aspects of the taxi-drive, the stochastic process implied by the puzzle), but an analytic solution remains elusive.

                   

The darkweb: a social network anomaly

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The darkweb is unusual; about 87% of its sites never link to another site. To call it a “web” is thus a misnomer – it’s better described as a set of largely isolated dark silos. This topology is highly dissimilar to other social networks and indicates darkweb users behave much differently to www users. Preferential attachment can partially explain the strange topology of the darkweb, but a more accurate model based on the social behavior of its users is lacking. Data here.

                         

Swarmalators: oscillators that sync and swarm

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Synchronization occurs in many natural and technological systems, from cardiac pacemaker cells to coupled lasers. In the synchronized state, the individual cells or lasers coordinate the timing of their oscillations, but they do not move through space. A complementary form of self-organization occurs among swarming insects, flocking birds, or schooling fish; now the individuals move through space, but without conspicuously altering their internal states.

Yet in some systems – such as groups of sperm, Japanese tree frogs, and colloidal suspensions of magnetic particles – self assembly and synchronization occur together. In this project, we investigate the co-action of these twin forms of self-orgnaization. You can find a fun demo here and here

Python code here. Mathematica code here.

Swarmalators have also been realized in the lab: 2D, 2D & 3D

       

Pulse coupled oscillators

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During every heartbeat, thousands of pacemaker cells discharge all-at-once. This collective firing causes the contraction of cardiac muscles, which pumps blood around the body. Should these firing fall out of step, heartbeats can become erratic, inhibiting blood flow. In order to maintain healthy heart function, the pacemaker cells must therefore forever maintain their synchronous firing.

But how, precisely, do they do so? How do groups of cells stay organized enough to keep your heart beating? In this project, we try to figure this out – see this paper and this paper.