# Designing tie knots by random walks

T. Fink, Y. Mao

*Nature* 398, 31 (209)

#tieknots#randomwalks#combinatorics

The number of ways to tie a tie can be enumerated by counting the number of persistent random walks on a triangular lattice.

We developed a mathematical model of tie knots, and provide a map between tie knots and persistent random walks on a triangular lattice. We classify knots according to their size and shape, and quantify the number of knots in each class. The optimal knot in a class is selected by the proposed aesthetic conditions of symme- try and balance. Of the 85 knots that can be tied with a conventional tie, we recover the four knots that are in widespread use and introduce six new aesthetically pleasing knots.

#### Degree-correlations in a bursting dynamic network model

F. Vanni, P. Barucca

*Journal of Economic Interaction and Coordination*

#### Phase transition creates the geometry of the continuum from discrete space

R. Farr, T. Fink

*Physical Review E*

#### Intelligently chosen interventions have potential to outperform the diode bridge in power conditioning

F. Liu, Y. Zhang, O. Dahlsten, F. Wang

*Scientific Reports *

#### Portfolio analysis and geographical allocation of renewable sources: A stochastic approach

A. Scala, A. Facchini, U. Perna, R. Basosi

*Energy Policy*

#### Changes to Gate Closure and its impact on wholesale electricity prices: The case of the UK

A. Facchini, A. Rubino, G. Caldarelli, G. Liddo

*Energy Policy*

#### The statistical physics of real-world networks

G. Cimini, T. Squartini, F. Saracco, D. Garlaschelli, A. Gabrielli, G. Caldarelli

*Nature Reviews Physics*

#### PopRank: Ranking pages’ impact and users’ engagement on Facebook

A. Zaccaria, M. Vicario, W. Quattrociocchi, A. Scala, L. Pietronero

*PLoS ONE *

128 / 128 papers