89 citations · 298 across the 11 of their papers we have counts for
11 papers
Defining the prime numbers prior to the integers: A first-principles approach to the distribution of primes
Kolbjørn Tunstrøm
While the prime numbers have been subject to mathematical inquiry since the ancient Greeks, the accumulated effort of understanding these numbers has - as Marcus du Sautoy recently…
The impact of anticipation in dynamical systems
P. Gerlee, K. Tunstrøm, T. Lundh +1
Collective motion in biology is often modelled as a dynamical system, in which individuals are represented as particles whose interactions are determined by the current state of th…
Primes in the intervals between primes squared
Kolbjørn Tunstrøm
The set of short intervals between consecutive primes squared has the pleasant---but seemingly unexploited---property that each interval is full…
The origin of the logarithmic integral in the prime number theorem
Kolbjørn Tunstrøm
We establish why li(x) outperforms x/log x as an estimate for the prime counting function pi(x). The result follows from subdividing the natural numbers into the intervals s_k :={p…
Collective dynamics of self-propelled particles with variable speed
Shradha Mishra, Kolbjørn Tunstrøm, Iain D. Couzin +1
Understanding the organization of collective motion in biological systems is an ongoing challenge. In this Paper we consider a minimal model of self-propelled particles with variab…
Determining interaction rules in animal swarms
Anders Eriksson, Martin Nilsson Jacobi, Johan Nystrom +1
In this paper we introduce a method for determining local interaction rules in animal swarms. The method is based on the assumption that the behavior of individuals in a swarm can…