How Turing parasites expand the computational landscape of digital life

Why are living systems complex? Why does the biosphere contain living beings with complexity features beyond those of the simplest replicators? What kind of evolutionary pressures result in more complex life forms? These are key questions that pervade the problem of how complexity arises in evolution. One particular way of tackling this is grounded in an algorithmic description of life: living organisms can be seen as systems that extract and process information from their surroundings in order to reduce uncertainty. Here we take this computational approach using a simple bit string model of coevolving agents and their parasites. While agents try to predict their worlds, parasites do the same with their hosts. The result of this process is that, in order to escape their parasites, the host agents expand their computational complexity despite the cost of maintaining it. This, in turn, is followed by increasingly complex parasitic counterparts. Such arms races display several qualitative phases, from monotonous to punctuated evolution or even ecological collapse. Our minimal model illustrates the relevance of parasites in providing an active mechanism for expanding living complexity beyond simple replicators, suggesting that parasitic agents are likely to be a major evolutionary driver for biological complexity.Comment: 13 pages, 8 main figures, 1 appendix with 5 extra figure

Layering in the Ising model

We consider the three-dimensional Ising model in a half-space with a boundary field (no bulk field). We compute the low-temperature expansion of layering transition lines

A linear construction for certain Kerdock and Preparata codes

The Nordstrom-Robinson, Kerdock, and (slightly modified) Pre\- parata codes are shown to be linear over \ZZ_4, the integers $\bmod~4$. The Kerdock and Preparata codes are duals over \ZZ_4, and the Nordstrom-Robinson code is self-dual. All these codes are just extended cyclic codes over \ZZ_4. This provides a simple definition for these codes and explains why their Hamming weight distributions are dual to each other. First- and second-order Reed-Muller codes are also linear codes over \ZZ_4, but Hamming codes in general are not, nor is the Golay code.Comment: 5 page

Scale-free Networks from Optimal Design

A large number of complex networks, both natural and artificial, share the presence of highly heterogeneous, scale-free degree distributions. A few mechanisms for the emergence of such patterns have been suggested, optimization not being one of them. In this letter we present the first evidence for the emergence of scaling (and smallworldness) in software architecture graphs from a well-defined local optimization process. Although the rules that define the strategies involved in software engineering should lead to a tree-like structure, the final net is scale-free, perhaps reflecting the presence of conflicting constraints unavoidable in a multidimensional optimization process. The consequences for other complex networks are outlined.Comment: 6 pages, 2 figures. Submitted to Europhysics Letters. Additional material is available at http://complex.upc.es/~sergi/software.ht

Some asymptotic properties of duplication graphs

Duplication graphs are graphs that grow by duplication of existing vertices, and are important models of biological networks, including protein-protein interaction networks and gene regulatory networks. Three models of graph growth are studied: pure duplication growth, and two two-parameter models in which duplication forms one element of the growth dynamics. A power-law degree distribution is found to emerge in all three models. However, the parameter space of the latter two models is characterized by a range of parameter values for which duplication is the predominant mechanism of graph growth. For parameter values that lie in this ``duplication-dominated'' regime, it is shown that the degree distribution either approaches zero asymptotically, or approaches a non-zero power-law degree distribution very slowly. In either case, the approach to the true asymptotic degree distribution is characterized by a dependence of the scaling exponent on properties of the initial degree distribution. It is therefore conjectured that duplication-dominated, scale-free networks may contain identifiable remnants of their early structure. This feature is inherited from the idealized model of pure duplication growth, for which the exact finite-size degree distribution is found and its asymptotic properties studied.Comment: 19 pages, including 3 figure

Liquid phase epitaxy and spectroscopic investigation of optically active KYb(WO4)2 thin layers

In recent years, Yb3+ has attracted much attention as an activating ion because of its small quantum defect for laser emission from 2F5/2 to 2F7/2 at ~1.03 µm, which provides high efficiency and reduced heat generation. A promising material for Yb3+ lasers is KYb(WO4)2 (KYbW) [1]. It can be grown from high-temperature solutions [2]. A suitable substrate material for the growth of single-crystalline layers with thicknesses in the range of the absorption length of ~13 µm at 981 nm is KY(WO4)2 (KYW).\ud We demonstrate the liquid phase epitaxy (LPE) of KYbW layers at start temperatures as low as 520°C from the chloride solvent KCl-NaCl-CsCl. This temperature is favorable in order to decrease the thermal stresses due to the differences in the thermal expansion coefficients of substrate and layer. Moreover, the choice of [010]-oriented KYW substrates bypasses the large difference in the thermal expansion coefficient along the [010] direction. Our spectroscopic investigations show that the fluorescence lifetime of ~250 µs measured in our LPE-grown KYbW layers is dominated by radiative decay and is very similar to that measured in top-seeded-solution-grown bulk samples [2]. Fast energy migration among the Yb3+ ions and energy transfer to small amounts of Tm3+ and Er3+ ions present in the YbCl3 reagent lead to visible upconversion luminescence in the layers under 981-nm excitation.\ud \ud [1] P. Klopp, U. Griebner, V. Petrov, X. Mateos, M.A. Bursukova, M.C. Pujol, R. Solé, J. Gavaldà, M. Aguiló, F. Güell, J. Massons, T. Kirilov, F. Díaz, Appl. Phys. B 2002, 74, 185\ud [2] M.C. Pujol, M.A. Bursukova, F. Güell, X. Mateos, R. Solé, J. Gavaldà, M. Aguiló, J. Massons, F. Díaz, P. Klopp, U. Griebner, V. Petrov, Phys. Rev. B 2002, 65, 16512

Topological reversibility and causality in feed-forward networks

Systems whose organization displays causal asymmetry constraints, from evolutionary trees to river basins or transport networks, can be often described in terms of directed paths (causal flows) on a discrete state space. Such a set of paths defines a feed-forward, acyclic network. A key problem associated with these systems involves characterizing their intrinsic degree of path reversibility: given an end node in the graph, what is the uncertainty of recovering the process backwards until the origin? Here we propose a novel concept, \textit{topological reversibility}, which rigorously weigths such uncertainty in path dependency quantified as the minimum amount of information required to successfully revert a causal path. Within the proposed framework we also analytically characterize limit cases for both topologically reversible and maximally entropic structures. The relevance of these measures within the context of evolutionary dynamics is highlighted.Comment: 9 pages, 3 figure