A new dimension to Turing patterns

It is well known that simple reaction-diffusion systems can display very rich pattern formation behavior. Here we have studied two examples of such systems in three dimensions. First we investigate the morphology and stability of a generic Turing system in three dimensions and then the well-known Gray-Scott model. In the latter case, we added a small number of morphogen sources in the system in order to study its robustness and the formation of connections between the sources. Our results raise the question of whether Turing patterning can produce an inductive signaling mechanism for neuronal growth.Comment: Movies available here at http://www.lce.hut.fi/research/polymer/turing.shtm

Dynamics of deceptive interactions in social networks

In this paper we examine the role of lies in human social relations by implementing some salient characteristics of deceptive interactions into an opinion formation model, so as to describe the dynamical behaviour of a social network more realistically. In this model we take into account such basic properties of social networks as the dynamics of the intensity of interactions, the influence of public opinion, and the fact that in every human interaction it might be convenient to deceive or withhold information depending on the instantaneous situation of each individual in the network. We find that lies shape the topology of social networks, especially the formation of tightly linked, small communities with loose connections between them. We also find that agents with a larger proportion of deceptive interactions are the ones that connect communities of different opinion, and in this sense they have substantial centrality in the network. We then discuss the consequences of these results for the social behaviour of humans and predict the changes that could arise due to a varying tolerance for lies in society.Comment: 17 pages, 8 figures; Supplementary Information (3 pages, 1 figure

Are Opinions Based on Science: Modelling Social Response to Scientific Facts

As scientists we like to think that modern societies and their members base their views, opinions and behaviour on scientific facts. This is not necessarily the case, even though we are all (over-) exposed to information flow through various channels of media, i.e. newspapers, television, radio, internet, and web. It is thought that this is mainly due to the conflicting information on the mass media and to the individual attitude (formed by cultural, educational and environmental factors), that is, one external factor and another personal factor. In this paper we will investigate the dynamical development of opinion in a small population of agents by means of a computational model of opinion formation in a co-evolving network of socially linked agents. The personal and external factors are taken into account by assigning an individual attitude parameter to each agent, and by subjecting all to an external but homogeneous field to simulate the effect of the media. We then adjust the field strength in the model by using actual data on scientific perception surveys carried out in two different populations, which allow us to compare two different societies. We interpret the model findings with the aid of simple mean field calculations. Our results suggest that scientifically sound concepts are more difficult to acquire than concepts not validated by science, since opposing individuals organize themselves in close communities that prevent opinion consensus.Comment: 21 pages, 5 figures. Submitted to PLoS ON

Dynamic asset trees and Black Monday

The minimum spanning tree, based on the concept of ultrametricity, is constructed from the correlation matrix of stock returns. The dynamics of this asset tree can be characterised by its normalised length and the mean occupation layer, as measured from an appropriately chosen centre called the `central node'. We show how the tree length shrinks during a stock market crisis, Black Monday in this case, and how a strong reconfiguration takes place, resulting in topological shrinking of the tree.Comment: 6 pages, 3 eps figues. Elsevier style. Will appear in Physica A as part of the Bali conference proceedings, in pres

Bayesian exponential family projections for coupled data sources

Exponential family extensions of principal component analysis (EPCA) have received a considerable amount of attention in recent years, demonstrating the growing need for basic modeling tools that do not assume the squared loss or Gaussian distribution. We extend the EPCA model toolbox by presenting the first exponential family multi-view learning methods of the partial least squares and canonical correlation analysis, based on a unified representation of EPCA as matrix factorization of the natural parameters of exponential family. The models are based on a new family of priors that are generally usable for all such factorizations. We also introduce new inference strategies, and demonstrate how the methods outperform earlier ones when the Gaussianity assumption does not hold

Space--Time Tradeoffs for Subset Sum: An Improved Worst Case Algorithm

The technique of Schroeppel and Shamir (SICOMP, 1981) has long been the most efficient way to trade space against time for the SUBSET SUM problem. In the random-instance setting, however, improved tradeoffs exist. In particular, the recently discovered dissection method of Dinur et al. (CRYPTO 2012) yields a significantly improved space--time tradeoff curve for instances with strong randomness properties. Our main result is that these strong randomness assumptions can be removed, obtaining the same space--time tradeoffs in the worst case. We also show that for small space usage the dissection algorithm can be almost fully parallelized. Our strategy for dealing with arbitrary instances is to instead inject the randomness into the dissection process itself by working over a carefully selected but random composite modulus, and to introduce explicit space--time controls into the algorithm by means of a "bailout mechanism"