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Necktie knots are inherently topological structures; what makes them tractable is the particular manner in which they are constructed. This observation motivates a map between tie knots andâ€¦ (More)

- Bernard Derrida, Thomas M. A. Fink
- Physical review letters
- 2002

Assembling fragments randomly sampled from along a sequence is the basis of whole-genome shotgun sequencing, a technique used to map the DNA of the human and other genomes. We calculate theâ€¦ (More)

- Sebastian E. Ahnert, Karen Willbrand, Francis C. S. Brown, Thomas M. A. Fink
- Bioinformatics
- 2006

MOTIVATION
Following the advent of microarray technology in recent years, the challenge for biologists is to identify genes of interest from the thousands of genetic expression levels measured inâ€¦ (More)

- Sebastian E. Ahnert, Thomas M. A. Fink, Andrei Zinovyev
- Journal of theoretical biology
- 2008

Despite tremendous advances in the field of genomics, the amount and function of the large non-coding part of the genome in higher organisms remains poorly understood. Here we report an observation,â€¦ (More)

Real-world social and economic networks typically display a number of particular topological properties, such as a giant connected component, a broad degree distribution, the small-world property andâ€¦ (More)

- Francis C. S. Brown, Thomas M. A. Fink, Karen Willbrand
- Discrete Mathematics
- 2007

Let = ( 1, . . . , N), where i = Â±1, and let C( ) denote the number of permutations of 1, 2, . . . , N + 1, whose upâ€“down signature sign( (i + 1) âˆ’ (i)) = i , for i = 1, . . . , N . We prove that theâ€¦ (More)

We study the simplest random landscape, the curve formed by joining consecutive data points f1, . . . , fN+1 with line segments, where the fi are i.i.d. random numbers and fi = fj . We label eachâ€¦ (More)

- Sebastian E. Ahnert, Thomas M. A. Fink
- Journal of the Royal Society, Interface
- 2016

Network motifs have been studied extensively over the past decade, and certain motifs, such as the feed-forward loop, play an important role in regulatory networks. Recent studies have used Booleanâ€¦ (More)

- Robin C. Ball, Thomas M. A. Fink
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2002

We consider the design of proteins to be simultaneously thermodynamically stable in multiple independent and correlated conformations. We first show that a protein can be trained to fold to multipleâ€¦ (More)

A cellular automaton is a collection of cells, each of which is in one of a finite number of states. The cellsâ€™ states are updated according to some local rules which take into account the state ofâ€¦ (More)