# Research

## Mutations spreading through a network

In fields ranging from cancer biology to evolutionary game theory, it’s important to understand how a tiny group of mutants can spread and ultimately take over a much larger population of normal individuals. How does the time for mutant takeover depend on the network structure of the population? Mathematical models provide an answer, and may explain why the incubation periods for many diseases show strongly right-skewed distributions, with some people taking much longer than others to show symptoms.

## More

- Articles
- Evolutionary Dynamics of Incubation Periods (PDF)
*– eLife* - Takeover Times for a Simple Model of Network Infection (PDF)
*– Physical Review E*

- Press
- Why Don’t Patients Get Sick in Sync? Modelers Find Statistical Clues
*– Quanta Magazine*

## How one new thing leads to another

The old adage that one thing leads to another may have surprising scientific implications for anything that evolves. By opening new possibilities, a novelty or innovation can pave the way for others in a process that Stuart Kauffman has called ‘‘expanding the adjacent possible.” Strogatz and his colleagues have taken a first step toward modeling the adjacent possible mathematically and exploring its role in biological, cultural, and technological evolution.

## More

- Articles
- The Dynamics of Correlated Novelties (PDF)
*– Scientific Reports* - Dynamics on Expanding Spaces: Modeling the Emergence of Novelties (PDF)
*– Creativity and Universality in Language*

- Press
- Mathematical Model Reveals the Patterns of How Innovations Arise
*– Technology Review* - The Mathematics of Discovering New Things
*– The Washington Post* - The Mathematics of Novelties and Innovations
*– Wired.com*

## Urban mobility

What’s the minimum number of taxis it would take to meet the demand in New York City, if the cabs were dispatched optimally? 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.

## More

- Articles
- Quantifying the Benefits of Vehicle Pooling With Shareability Networks (PDF)
*– Proceedings of the National Academy of Sciences* - Scaling Law of Urban Ride Sharing (PDF)
*– Scientific Reports* - Addressing the Minimum Fleet Problem in On-Demand Urban Mobility
*– Nature*

- Press
- If Two New Yorkers Shared a Cab...
*– The New York Times* - Optimizing Taxi Fleet Size the Subject of Multi-University Research
*– Cornell Chronicle* - Taxi-sharing in Cities Follows Universal Maths Law
*– Nature*

## Dynamics of social balance

“The enemy of my enemy is my friend” – what are the mathematical consequences of playing out this logic in large social or political networks? Tools from statistical physics, graph theory, and random matrix theory bring out the surprising implications of this ancient approach to friendship and rivalry.

## More

- Articles
- Energy Landscape of Social Balance (PDF)
*– Physical Review Letters* - Continuous-Time Model of Structural Balance (PDF)
*– Proceedings of the National Academy of Sciences*

- Press
- Physics Model Determines Dynamics of Friends and Enemies
*– Phys.org*

## Dynamics of political moderation

In a simple model of a society polarized by ideological conflict, how can moderation be encouraged? Under what conditions will a committed minority of true believers eventually win everyone over to their point of view?

## More

- Articles
- Encouraging Moderation: Clues From a Simple Model of Ideological Conflict (PDF)
*– Physical Review Letters*

- Press
- Why Moderate Beliefs Rarely Prevail (PDF)
*– Phys.org*

## Chimera states for coupled oscillators

Systems of identical oscillators with symmetrical coupling can sometimes split into two domains, one synchronized, the other desynchronized. The properties of such a “chimera state” have been elucidated by exactly solvable models.

## More

- Articles
- Chimera States for Coupled Oscillators (PDF)
*– Physical Review Letters* - Solvable Model for Chimera States of Coupled Oscillators (PDF)
*– Physical Review Letters* - Solvable Model of Spiral Wave Chimeras (PDF)
*– Physical Review Letters*

- Press
- Exotic Chimera Dynamics Glimpsed in Experiments
*– Physics Today* - News and Views: Spontaneous Synchrony Breaking
*– Nature Physics*

## Crowd synchronization on the Millennium Bridge

What caused London’s Millennium Bridge to wobble on its opening day? And why did the pedestrians on it inadvertently fall into step with its sideways vibrations? A model based on ideas from mathematical biology explains both effects as two sides of the same coin.

## More

- Articles
- Crowd Synchrony on the Millennium Bridge (PDF)
*– Nature** supplementary information (PDF)

- Press
- All Together Now: Synchrony Explains Swaying
*– The New York Times* - Few People 'Caused' Bridge Wobble
*– BBC News* - Explaining Why the Millennium Bridge Wobbled
*– Science Daily* - Revealed: Why London's Millennium Bridge Wobbled
*– Reuters* - Millennium Bridge Wobbles Are Explained at Last
*– The Telegraph* - Millennium Bridge Wobble Explained
*– Financial Times*

## Dynamics of language death

The world’s languages are vanishing at an alarming rate. Modeling the competition between languages with the tools of population dynamics led to the first quantitative model of language decline.

## More

- Articles
- Modelling the Dynamics of Language Death (PDF)
*– Nature*

- Press
- 'Status' Drives Extinction of Languages
*– ABC Science* - Gaelic 'Extinct in 40 Years'
*– Scottish Daily Record* - Language's Status Drives its Survival
*– Discovery News*

## Percolation on random graphs

Mathematical studies of the Internet, social networks, and the power grid have addressed the resilience of these networks to either random or targeted deletion of network nodes. Percolation models on random graphs with arbitrary degree distributions can be solved exactly to illuminate this issue of network resilience.

## More

- Articles
- Network Robustness and Fragility: Percolation on Random Graphs (PDF)
*– Physical Review Letters* - Random Graphs with Arbitrary Degree Distribution and Their Applications (PDF)
*– Physical Review E*

- Press
- What Happens When 99% of the Net Crashes?
*– Slashdot*

## Small-world networks

How can all seven billion of us be just six handshakes apart? “Small-world networks,” introduced by Strogatz and his former graduate student Duncan Watts, give one possible explanation. The same math also gives insight into how epidemics spread, how brains are wired, and how blackouts propagate through the power grid.

## More

- Articles
- Collective Dynamics of 'Small-World' Networks (PDF)
*– Nature*

- Press
- It's a Small World
*– Nature News and Views* - Mathematicians Prove That It's a Small World
*– The New York Times* - Small World (PDF)
*– Cornell Magazine*

## Dynamics of Josephson junction arrays

Josephson junctions are superconducting electronic devices that obey the same governing equations as pendulums – but they swing a hundred billion times faster. When thousands of them interact, how do they behave?

## More

- Articles
- Synchronization Transitions in a Disordered Josephson Series Array (PDF)
*– Physical Review Letters*

- Press
- Keeping the Beat (PDF)
*– Science News*

## Sending secret messages with synchronized chaos

A pair of synchronized chaotic circuits can be used to create a new kind of communication system. Moreover, a message becomes more private when it’s cloaked in chaos.

## More

- Articles
- Synchronization of Lorenz-Based Chaotic Circuits, With Applications to Communications (PDF)
*– IEEE Transactions on Circuits and Systems*

- Press
- Coming In Loud and Clear – Via Chaos (PDF)
*– Science*

## Dynamics of switching in charge-density waves

A charge-density wave is like a block of jello on a sticky plate. If you tug it sideways, it stays stuck in place … unless you tug it just hard enough; then it breaks loose and starts to slide. A coupled oscillator model showed that the sliding speed could depend discontinuously on the tugging force – as previously seen experimentally.

## More

- Articles
- Simple Model of Collective Transport With Phase Slippage (PDF)
*– Physical Review Letters* - Collective Dynamics of Coupled Oscillators With Random Pinning (PDF)
*– Physica D* - Delayed Switching in a Phase-Slip Model of Charge-Density Wave Transport (PDF)
*– Physical Review B*

## Synchronization of coupled oscillators

How can thousands of fireflies flash on and off in unison, all night long, without any leader or cue from the environment? More generally, how can dissimilar oscillators all come to act as one, in diverse biological, physical, and chemical systems? Over two decades of work on modeling such systems, using nonlinear dynamics, statistical physics, and computer simulations, has deepened our understanding of synchrony in our bodies and the world around us.

## More

- Articles
- Synchronization of Pulse-Coupled Biological Oscillators (PDF)
*– SIAM Journal on Applied Mathematics* - Coupled Oscillators and Biological Synchronization (PDF)
*– Scientific American* - From Kuramoto to Crawford: Exploring the Onset of Synchronization in Populations of Coupled Oscillators (PDF)
*– Physica D*

- Press
- All Together Now (PDF)
*– Nature* - All Together Now (PDF)
*– Nature* - Step in Time (PDF)
*– Science News* - Flirting Male Crabs Found to Wave Claws in Unison
*– The New York Times* - A Mystery of Nature: Mangroves Full of Fireflies Blinking in Unison
*– The New York Times*

## Data analysis of human sleep and circadian rhythms

Studies of brave volunteers living for months in underground caves or windowless apartments have clarified how bright light shifts our circadian rhythms, why many of us like to take an afternoon nap, and why it's so hard to fall asleep two hours before your regular bedtime.

## More

- Articles
- Bright Light Resets the Human Circadian Pacemaker Independent of the Timing of the Sleep-Wake Cycle
*– Science* - Circadian Pacemaker Interferes With Sleep Onset at Specific Times Each Day: Role in Insomnia
*– American Journal of Physiology*

- Press
- Daily Rhythms Running Like Clockwork
*– Science News*

## Topology of scroll waves

Spiral waves of activity occur in thin layers of heart muscle, nerve tissue, and certain chemical reactions. Scroll waves, their three-dimensional cousins, can be twisted, linked, and knotted according to a topological exclusion principle.

## More

- Articles
- Organizing Centres for Three-Dimensional Chemical Waves (PDF)
*– Nature* - Yeast Oscillations, Belousov-Zhabotinsky Waves, and the Non-Retraction Theorem (PDF)
*– Mathematical Intelligencer*

- Press
- Strange, Scroll-Like Wave Is Linked to Biological Processes
*– The New York Times*

## Topology of chromatin and supercoiled DNA

The linking number of DNA helps us unravel the structure of the chromatin fiber, the next level of coiling above the double helix and below the chromosome.

## More

- Articles
- Structure of Chromatin and the Linking Number of DNA (PDF)
*– Proceedings of the National Academy of Sciences*

Einstein's boyhood proof of the Pythagorean theorem foreshadows the scientist he later became.

- The New YorkerNovember 19, 2015