Sebastian Bernhardsson

Zipf's law unzipped

Why does Zipfs law give a good description of data from seemingly completely unrelated phenomena? Here it is argued that the reason is that they can all be described as outcomes of a ubiquitous ra ...

The meta book and size-dependent properties of written language

Evidence is given for a systematic text-length dependence of the power-law index

Flow Improvement Caused by Agents Who Ignore Traffic Rules

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Equilibrium strategy and population-size effects in lowest unique bid auctions.

of a single book. The estimated

Size dependent word frequencies and translational invariance of books

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Neutral theory of chemical reaction networks

values are consistent with a monotonic decrease from 2 to 1 with i ...

The Blind Watchmaker Network: Scale-Freeness and Evolution

A system of agents moving along a road in both directions is studied numerically within a cellular-automata formulation. An agent steps to the right with probability q or to the left with 1-q when encountering other agents. Our model is restricted to two agent types, traffic-rule abiders (q=1) and traffic-rule ignorers (q=1/2) , and the traffic flow, resulting from the interaction between these two types of agents, which is obtained as a function of density and relative fraction. The risk for jamming at a fixed density, when starting from a disordered situation, is smaller when every agent abides by a traffic rule than when all agents ignore the rule. Nevertheless, the absolute minimum occurs when a small fraction of ignorers are present within a majority of abiders. The characteristic features for the spatial structure of the flow pattern are obtained and discussed.

Degree landscapes in scale-free networks

In lowest unique bid auctions, N players bid for an item. The winner is whoever places the lowest bid, provided that it is also unique. We use a grand canonical approach to derive an analytical expression for the equilibrium distribution of strategies. We then study the properties of the solution as a function of the mean number of players, and compare them with a large data set of internet auctions. The theory agrees with the data with striking accuracy for small population-size N, while for larger N a qualitatively different distribution is observed. We interpret this result as the emergence of two different regimes, one in which adaptation is feasible and one in which it is not. Our results question the actual possibility of a large population to adapt and find the optimal strategy when participating in a collective game.

Models and average properties of scale-free directed networks

It is shown that a real novel shares many characteristic features with a null model in which the words are randomly distributed throughout the text. Such a common feature is a certain translational invariance of the text. Another is that the functional form of the word-frequency distribution of a novel depends on the length of the text in the same way as the null model. This means that an approximate power-law tail ascribed to the data will have an exponent which changes with the size of the text-section which is analyzed. A further consequence is that a novel cannot be described by text-evolution models such as the Simon model. The size-transformation of a novel is found to be well described by a specific Random Book Transformation. This size transformation in addition enables a more precise determination of the functional form of the word-frequency distribution. The implications of the results are discussed.

Selective pressure on metabolic network structures as measured from the random blind-watchmaker network

To what extent do the characteristic features of a chemical reaction network reflect its purpose and function? In general, one argues that correlations between specific features and specific functions are key to understanding a complex structure. However, specific features may sometimes be neutral and uncorrelated with any system-specific purpose, function or causal chain. Such neutral features are caused by chance and randomness. Here we compare two classes of chemical networks: one that has been subjected to biological evolution (the chemical reaction network of metabolism in living cells) and one that has not (the atmospheric planetary chemical reaction networks). Their degree distributions are shown to share the very same neutral system-independent features. The shape of the broad distributions is to a large extent controlled by a single parameter, the network size. From this perspective, there is little difference between atmospheric and metabolic networks; they are just different sizes of the same random assembling network. In other words, the shape of the degree distribution is a neutral characteristic feature and has no functional or evolutionary implications in itself; it is not a matter of life and death.