📝 Taxi shareability
P Santi, G Resta, M Szell, S Sobolevsky, SH #Strogatz, C Ratti
📌 If people shared taxis with strangers, how much money could be saved? And how much could pollution and traffic be reduced? A dataset of 150 million taxi trips and a new type of mathematical analysis enabled the untapped potential of New York City’s fleet of more than 13,000 taxis to be quantified.
Press: goo.gl/r1RgW5
If Two New Yorkers Shared a Cab...
– The New York Times
Articles: goo.gl/lQvkAc
Quantifying the Benefits of Vehicle Pooling With Shareability Networks (PDF)
P Santi, G Resta, M Szell, S Sobolevsky, SH #Strogatz, C Ratti
📌 If people shared taxis with strangers, how much money could be saved? And how much could pollution and traffic be reduced? A dataset of 150 million taxi trips and a new type of mathematical analysis enabled the untapped potential of New York City’s fleet of more than 13,000 taxis to be quantified.
Press: goo.gl/r1RgW5
If Two New Yorkers Shared a Cab...
– The New York Times
Articles: goo.gl/lQvkAc
Quantifying the Benefits of Vehicle Pooling With Shareability Networks (PDF)
Nytimes
If 2 New Yorkers Shared a Cab ...
A team of mathematicians and engineers has calculated that if taxi riders were willing to share a cab, New York City could reduce the current fleet of 13,500 taxis up to 40 percent.
📝 Nonlinear dynamics of the rock-paper-scissors game with mutations
Danielle F. P. Toupo and Steven H. #Strogatz
goo.gl/wuaYmk
📌 Abstract
We analyze the replicator-mutator equations for the rock-paper-scissors game. Various graph-theoretic patterns of mutation are considered, ranging from a single unidirectional mutation pathway between two of the species, to global bidirectional mutation among all the species. Our main result is that the coexistence state, in which all three species exist in equilibrium, can be destabilized by arbitrarily small mutation rates. After it loses stability, the coexistence state gives birth to a stable limit cycle solution created in a supercritical Hopf bifurcation. This attracting periodic solution exists for all the mutation patterns considered, and persists arbitrarily close to the limit of zero mutation rate and a zero-sum game.
Danielle F. P. Toupo and Steven H. #Strogatz
goo.gl/wuaYmk
📌 Abstract
We analyze the replicator-mutator equations for the rock-paper-scissors game. Various graph-theoretic patterns of mutation are considered, ranging from a single unidirectional mutation pathway between two of the species, to global bidirectional mutation among all the species. Our main result is that the coexistence state, in which all three species exist in equilibrium, can be destabilized by arbitrarily small mutation rates. After it loses stability, the coexistence state gives birth to a stable limit cycle solution created in a supercritical Hopf bifurcation. This attracting periodic solution exists for all the mutation patterns considered, and persists arbitrarily close to the limit of zero mutation rate and a zero-sum game.
📝 Taxi pooling in New York City:
a #network-based approach to social sharing problems
Paolo Santi, Giovanni Resta, Michael Szell, Stanislav Sobolevsky, Steven #Strogatz, Carlo Ratti
goo.gl/mdS8Is
📌 Taxi services are a vital part of urban transportation, and a major contributor to traffic
congestion and air pollution causing substantial adverse effects on human health1, 2.
Sharing taxi trips is a possible way of reducing the negative impact of taxi services on
cities3, but this comes at the expense of passenger discomfort in terms of a longer travel
time. Due to computational challenges, taxi sharing has traditionally been approached on
small scales4, 5, such as within airport perimeters6, 7, or with dynamical ad-hoc ...
a #network-based approach to social sharing problems
Paolo Santi, Giovanni Resta, Michael Szell, Stanislav Sobolevsky, Steven #Strogatz, Carlo Ratti
goo.gl/mdS8Is
📌 Taxi services are a vital part of urban transportation, and a major contributor to traffic
congestion and air pollution causing substantial adverse effects on human health1, 2.
Sharing taxi trips is a possible way of reducing the negative impact of taxi services on
cities3, but this comes at the expense of passenger discomfort in terms of a longer travel
time. Due to computational challenges, taxi sharing has traditionally been approached on
small scales4, 5, such as within airport perimeters6, 7, or with dynamical ad-hoc ...
🗞 Takeover times for a simple model of network infection
Bertrand Ottino-Löffler, Jacob G. Scott, Steven H. #Strogatz
🔗 https://arxiv.org/pdf/1702.00881
📌ABSTRACT
We study a stochastic model of infection spreading on a network. At each time step a node is chosen at random, along with one of its neighbors. If the node is infected and the neighbor is susceptible, the neighbor becomes infected. How many time steps T does it take to completely infect a network of Nnodes, starting from a single infected node? An analogy to the classic "coupon collector" problem of probability theory reveals that the takeover time T is dominated by extremal behavior, either when there are only a few infected nodes near the start of the process or a few susceptible nodes near the end. We show that for N≫1, the takeover time T is distributed as a Gumbel for the star graph; as the sum of two Gumbels for a complete graph and an Erd\H{o}s-R\'{e}nyi random graph; as a normal for a one-dimensional ring and a two-dimensional lattice; and as a family of intermediate skewed distributions for d-dimensional lattices with d≥3 (these distributions approach the sum of two Gumbels as d approaches infinity). Connections to evolutionary dynamics, cancer, incubation periods of infectious diseases, first-passage percolation, and other spreading phenomena in biology and physics are discussed.
Bertrand Ottino-Löffler, Jacob G. Scott, Steven H. #Strogatz
🔗 https://arxiv.org/pdf/1702.00881
📌ABSTRACT
We study a stochastic model of infection spreading on a network. At each time step a node is chosen at random, along with one of its neighbors. If the node is infected and the neighbor is susceptible, the neighbor becomes infected. How many time steps T does it take to completely infect a network of Nnodes, starting from a single infected node? An analogy to the classic "coupon collector" problem of probability theory reveals that the takeover time T is dominated by extremal behavior, either when there are only a few infected nodes near the start of the process or a few susceptible nodes near the end. We show that for N≫1, the takeover time T is distributed as a Gumbel for the star graph; as the sum of two Gumbels for a complete graph and an Erd\H{o}s-R\'{e}nyi random graph; as a normal for a one-dimensional ring and a two-dimensional lattice; and as a family of intermediate skewed distributions for d-dimensional lattices with d≥3 (these distributions approach the sum of two Gumbels as d approaches infinity). Connections to evolutionary dynamics, cancer, incubation periods of infectious diseases, first-passage percolation, and other spreading phenomena in biology and physics are discussed.